[{"data":1,"prerenderedAt":5234},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fmittelpunkt-schwerpunkt-vektoren":546,"formula-related-de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fmittelpunkt-schwerpunkt-vektoren":5221},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":556,"category":312,"checks":5150,"conditions":5183,"conditionsHtml":5183,"deprecated":5183,"description":5144,"extension":5184,"figure":5183,"figureCaption":5183,"figureHtml":5183,"formulaId":5185,"latex":5186,"latexHtml":5187,"level":5188,"meta":5189,"navigation":5190,"path":5191,"redirectFrom":5192,"related":5193,"seo":5198,"stem":5199,"subject":589,"summary":5200,"tags":5201,"variables":5207,"__hash__":5220},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fmittelpunkt-schwerpunkt-vektoren.md","Mittelpunkt und Schwerpunkt mit Vektoren",[550,551,552,553,554,555],"Mittelpunkt einer Strecke im Raum","Schwerpunkt Dreieck Vektoren","Schwerpunkt im Raum berechnen","Mittelpunkt Ortsvektor","Seitenhalbierende Schwerpunkt","Schwerpunkt Tetraeder",{"type":557,"value":558,"toc":5143},"minimark",[559,564,568,1394,1785,1788,1792,1982,2598,2729,3346,3919,4521,4525],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567],"p",{},"Mit Ortsvektoren lassen sich besondere Punkte im Raum direkt berechnen, komponentenweise:",[569,570,571,1262],"ul",{},[572,573,574,578,579,626,627,664,665,693,694,722,723,1261],"li",{},[575,576,577],"strong",{},"Mittelpunkt"," ",[580,581,584,606],"span",{"className":582},[583],"katex",[580,585,588],{"className":586},[587],"katex-mathml",[589,590,592],"math",{"xmlns":591},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[593,594,595,602],"semantics",{},[596,597,598],"mrow",{},[599,600,601],"mi",{},"M",[603,604,601],"annotation",{"encoding":605},"application\u002Fx-tex",[580,607,611],{"className":608,"ariaHidden":610},[609],"katex-html","true",[580,612,615,620],{"className":613},[614],"base",[580,616],{"className":617,"style":619},[618],"strut","height:0.6833em;",[580,621,601],{"className":622,"style":625},[623,624],"mord","mathnormal","margin-right:0.109em;"," der Strecke ",[580,628,630,648],{"className":629},[583],[580,631,633],{"className":632},[587],[589,634,635],{"xmlns":591},[593,636,637,645],{},[596,638,639,642],{},[599,640,641],{},"A",[599,643,644],{},"B",[603,646,647],{"encoding":605},"AB",[580,649,651],{"className":650,"ariaHidden":610},[609],[580,652,654,657,660],{"className":653},[614],[580,655],{"className":656,"style":619},[618],[580,658,641],{"className":659},[623,624],[580,661,644],{"className":662,"style":663},[623,624],"margin-right:0.0502em;",": Man geht von ",[580,666,668,681],{"className":667},[583],[580,669,671],{"className":670},[587],[589,672,673],{"xmlns":591},[593,674,675,679],{},[596,676,677],{},[599,678,641],{},[603,680,641],{"encoding":605},[580,682,684],{"className":683,"ariaHidden":610},[609],[580,685,687,690],{"className":686},[614],[580,688],{"className":689,"style":619},[618],[580,691,641],{"className":692},[623,624]," aus den halben Weg nach ",[580,695,697,710],{"className":696},[583],[580,698,700],{"className":699},[587],[589,701,702],{"xmlns":591},[593,703,704,708],{},[596,705,706],{},[599,707,644],{},[603,709,644],{"encoding":605},[580,711,713],{"className":712,"ariaHidden":610},[609],[580,714,716,719],{"className":715},[614],[580,717],{"className":718,"style":619},[618],[580,720,644],{"className":721,"style":663},[623,624],", ",[580,724,726,812],{"className":725},[583],[580,727,729],{"className":728},[587],[589,730,731],{"xmlns":591},[593,732,733,809],{},[596,734,735,745,748,755,758,768,779,781,787,791,797,799,806],{},[736,737,738,741],"mover",{"accent":610},[599,739,740],{},"m",[742,743,744],"mo",{},"⃗",[742,746,747],{},"=",[736,749,750,753],{"accent":610},[599,751,752],{},"a",[742,754,744],{},[742,756,757],{},"+",[759,760,761,765],"mfrac",{},[762,763,764],"mn",{},"1",[762,766,767],{},"2",[736,769,770,776],{"accent":610},[596,771,772,774],{},[599,773,641],{},[599,775,644],{},[742,777,778],{"stretchy":610},"→",[742,780,747],{},[759,782,783,785],{},[762,784,764],{},[762,786,767],{},[742,788,790],{"stretchy":789},"false","(",[736,792,793,795],{"accent":610},[599,794,752],{},[742,796,744],{},[742,798,757],{},[736,800,801,804],{"accent":610},[599,802,803],{},"b",[742,805,744],{},[742,807,808],{"stretchy":789},")",[603,810,811],{"encoding":605},"\\vec{m} = \\vec{a} + \\frac{1}{2}\\overrightarrow{AB} = \\frac{1}{2}(\\vec{a} + \\vec{b})",[580,813,815,889,942,1092,1214],{"className":814,"ariaHidden":610},[609],[580,816,818,822,877,882,886],{"className":817},[614],[580,819],{"className":820,"style":821},[618],"height:0.714em;",[580,823,826],{"className":824},[623,825],"accent",[580,827,830],{"className":828},[829],"vlist-t",[580,831,834],{"className":832},[833],"vlist-r",[580,835,838,849],{"className":836,"style":821},[837],"vlist",[580,839,841,846],{"style":840},"top:-3em;",[580,842],{"className":843,"style":845},[844],"pstrut","height:3em;",[580,847,740],{"className":848},[623,624],[580,850,851,854],{"style":840},[580,852],{"className":853,"style":845},[844],[580,855,859],{"className":856,"style":858},[857],"accent-body","left:-0.2355em;",[580,860,864],{"className":861,"style":863},[862],"overlay","height:0.714em;width:0.471em;",[865,866,873],"svg",{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.471em","0.714em","width:0.471em","0 0 471 714","xMinYMin",[874,875],"path",{"d":876},"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z",[580,878],{"className":879,"style":881},[880],"mspace","margin-right:0.2778em;",[580,883,747],{"className":884},[885],"mrel",[580,887],{"className":888,"style":881},[880],[580,890,892,896,931,935,939],{"className":891},[614],[580,893],{"className":894,"style":895},[618],"height:0.7973em;vertical-align:-0.0833em;",[580,897,899],{"className":898},[623,825],[580,900,902],{"className":901},[829],[580,903,905],{"className":904},[833],[580,906,908,916],{"className":907,"style":821},[837],[580,909,910,913],{"style":840},[580,911],{"className":912,"style":845},[844],[580,914,752],{"className":915},[623,624],[580,917,918,921],{"style":840},[580,919],{"className":920,"style":845},[844],[580,922,924],{"className":923,"style":858},[857],[580,925,927],{"className":926,"style":863},[862],[865,928,929],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,930],{"d":876},[580,932],{"className":933,"style":934},[880],"margin-right:0.2222em;",[580,936,757],{"className":937},[938],"mbin",[580,940],{"className":941,"style":934},[880],[580,943,945,949,1034,1083,1086,1089],{"className":944},[614],[580,946],{"className":947,"style":948},[618],"height:1.5503em;vertical-align:-0.345em;",[580,950,952,957,1030],{"className":951},[623],[580,953],{"className":954},[955,956],"mopen","nulldelimiter",[580,958,960],{"className":959},[759],[580,961,964,1021],{"className":962},[829,963],"vlist-t2",[580,965,967,1016],{"className":966},[833],[580,968,971,990,1001],{"className":969,"style":970},[837],"height:0.8451em;",[580,972,974,977],{"style":973},"top:-2.655em;",[580,975],{"className":976,"style":845},[844],[580,978,984],{"className":979},[980,981,982,983],"sizing","reset-size6","size3","mtight",[580,985,987],{"className":986},[623,983],[580,988,767],{"className":989},[623,983],[580,991,993,996],{"style":992},"top:-3.23em;",[580,994],{"className":995,"style":845},[844],[580,997],{"className":998,"style":1000},[999],"frac-line","border-bottom-width:0.04em;",[580,1002,1004,1007],{"style":1003},"top:-3.394em;",[580,1005],{"className":1006,"style":845},[844],[580,1008,1010],{"className":1009},[980,981,982,983],[580,1011,1013],{"className":1012},[623,983],[580,1014,764],{"className":1015},[623,983],[580,1017,1020],{"className":1018},[1019],"vlist-s","​",[580,1022,1024],{"className":1023},[833],[580,1025,1028],{"className":1026,"style":1027},[837],"height:0.345em;",[580,1029],{},[580,1031],{"className":1032},[1033,956],"mclose",[580,1035,1037],{"className":1036},[623,825],[580,1038,1040],{"className":1039},[829],[580,1041,1043],{"className":1042},[833],[580,1044,1047,1061],{"className":1045,"style":1046},[837],"height:1.2053em;",[580,1048,1049,1052],{"style":840},[580,1050],{"className":1051,"style":845},[844],[580,1053,1055,1058],{"className":1054},[623],[580,1056,641],{"className":1057},[623,624],[580,1059,644],{"className":1060,"style":663},[623,624],[580,1062,1066,1069],{"className":1063,"style":1065},[1064],"svg-align","top:-3.6833em;",[580,1067],{"className":1068,"style":845},[844],[580,1070,1074],{"className":1071,"style":1073},[1072],"hide-tail","height:0.522em;min-width:0.888em;",[865,1075,1080],{"xmlns":867,"width":1076,"height":1077,"viewBox":1078,"preserveAspectRatio":1079},"400em","0.522em","0 0 400000 522","xMaxYMin slice",[874,1081],{"d":1082},"M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z",[580,1084],{"className":1085,"style":881},[880],[580,1087,747],{"className":1088},[885],[580,1090],{"className":1091,"style":881},[880],[580,1093,1095,1099,1167,1170,1205,1208,1211],{"className":1094},[614],[580,1096],{"className":1097,"style":1098},[618],"height:1.1901em;vertical-align:-0.345em;",[580,1100,1102,1105,1164],{"className":1101},[623],[580,1103],{"className":1104},[955,956],[580,1106,1108],{"className":1107},[759],[580,1109,1111,1156],{"className":1110},[829,963],[580,1112,1114,1153],{"className":1113},[833],[580,1115,1117,1131,1139],{"className":1116,"style":970},[837],[580,1118,1119,1122],{"style":973},[580,1120],{"className":1121,"style":845},[844],[580,1123,1125],{"className":1124},[980,981,982,983],[580,1126,1128],{"className":1127},[623,983],[580,1129,767],{"className":1130},[623,983],[580,1132,1133,1136],{"style":992},[580,1134],{"className":1135,"style":845},[844],[580,1137],{"className":1138,"style":1000},[999],[580,1140,1141,1144],{"style":1003},[580,1142],{"className":1143,"style":845},[844],[580,1145,1147],{"className":1146},[980,981,982,983],[580,1148,1150],{"className":1149},[623,983],[580,1151,764],{"className":1152},[623,983],[580,1154,1020],{"className":1155},[1019],[580,1157,1159],{"className":1158},[833],[580,1160,1162],{"className":1161,"style":1027},[837],[580,1163],{},[580,1165],{"className":1166},[1033,956],[580,1168,790],{"className":1169},[955],[580,1171,1173],{"className":1172},[623,825],[580,1174,1176],{"className":1175},[829],[580,1177,1179],{"className":1178},[833],[580,1180,1182,1190],{"className":1181,"style":821},[837],[580,1183,1184,1187],{"style":840},[580,1185],{"className":1186,"style":845},[844],[580,1188,752],{"className":1189},[623,624],[580,1191,1192,1195],{"style":840},[580,1193],{"className":1194,"style":845},[844],[580,1196,1198],{"className":1197,"style":858},[857],[580,1199,1201],{"className":1200,"style":863},[862],[865,1202,1203],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,1204],{"d":876},[580,1206],{"className":1207,"style":934},[880],[580,1209,757],{"className":1210},[938],[580,1212],{"className":1213,"style":934},[880],[580,1215,1217,1221,1258],{"className":1216},[614],[580,1218],{"className":1219,"style":1220},[618],"height:1.2274em;vertical-align:-0.25em;",[580,1222,1224],{"className":1223},[623,825],[580,1225,1227],{"className":1226},[829],[580,1228,1230],{"className":1229},[833],[580,1231,1234,1242],{"className":1232,"style":1233},[837],"height:0.9774em;",[580,1235,1236,1239],{"style":840},[580,1237],{"className":1238,"style":845},[844],[580,1240,803],{"className":1241},[623,624],[580,1243,1245,1248],{"style":1244},"top:-3.2634em;",[580,1246],{"className":1247,"style":845},[844],[580,1249,1251],{"className":1250,"style":858},[857],[580,1252,1254],{"className":1253,"style":863},[862],[865,1255,1256],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,1257],{"d":876},[580,1259,808],{"className":1260},[1033],".",[572,1263,1264,578,1267,1297,1298,1339,1340,1393],{},[575,1265,1266],{},"Schwerpunkt",[580,1268,1270,1284],{"className":1269},[583],[580,1271,1273],{"className":1272},[587],[589,1274,1275],{"xmlns":591},[593,1276,1277,1282],{},[596,1278,1279],{},[599,1280,1281],{},"S",[603,1283,1281],{"encoding":605},[580,1285,1287],{"className":1286,"ariaHidden":610},[609],[580,1288,1290,1293],{"className":1289},[614],[580,1291],{"className":1292,"style":619},[618],[580,1294,1281],{"className":1295,"style":1296},[623,624],"margin-right:0.0576em;"," des Dreiecks ",[580,1299,1301,1320],{"className":1300},[583],[580,1302,1304],{"className":1303},[587],[589,1305,1306],{"xmlns":591},[593,1307,1308,1317],{},[596,1309,1310,1312,1314],{},[599,1311,641],{},[599,1313,644],{},[599,1315,1316],{},"C",[603,1318,1319],{"encoding":605},"ABC",[580,1321,1323],{"className":1322,"ariaHidden":610},[609],[580,1324,1326,1329,1332,1335],{"className":1325},[614],[580,1327],{"className":1328,"style":619},[618],[580,1330,641],{"className":1331},[623,624],[580,1333,644],{"className":1334,"style":663},[623,624],[580,1336,1316],{"className":1337,"style":1338},[623,624],"margin-right:0.0715em;",": der Schnittpunkt der drei Seitenhalbierenden. Er teilt jede Seitenhalbierende im Verhältnis ",[580,1341,1343,1362],{"className":1342},[583],[580,1344,1346],{"className":1345},[587],[589,1347,1348],{"xmlns":591},[593,1349,1350,1359],{},[596,1351,1352,1354,1357],{},[762,1353,767],{},[742,1355,1356],{},":",[762,1358,764],{},[603,1360,1361],{"encoding":605},"2 : 1",[580,1363,1365,1384],{"className":1364,"ariaHidden":610},[609],[580,1366,1368,1372,1375,1378,1381],{"className":1367},[614],[580,1369],{"className":1370,"style":1371},[618],"height:0.6444em;",[580,1373,767],{"className":1374},[623],[580,1376],{"className":1377,"style":881},[880],[580,1379,1356],{"className":1380},[885],[580,1382],{"className":1383,"style":881},[880],[580,1385,1387,1390],{"className":1386},[614],[580,1388],{"className":1389,"style":1371},[618],[580,1391,764],{"className":1392},[623],", von der Ecke aus gemessen.",[565,1395,1396,1397,1261],{},"Für die vier Ecken eines Tetraeders gilt entsprechend ",[580,1398,1400,1464],{"className":1399},[583],[580,1401,1403],{"className":1402},[587],[589,1404,1405],{"xmlns":591},[593,1406,1407,1461],{},[596,1408,1409,1416,1418,1425,1427,1433,1435,1441,1443,1450,1452,1459],{},[736,1410,1411,1414],{"accent":610},[599,1412,1413],{},"s",[742,1415,744],{},[742,1417,747],{},[759,1419,1420,1422],{},[762,1421,764],{},[762,1423,1424],{},"4",[742,1426,790],{"stretchy":789},[736,1428,1429,1431],{"accent":610},[599,1430,752],{},[742,1432,744],{},[742,1434,757],{},[736,1436,1437,1439],{"accent":610},[599,1438,803],{},[742,1440,744],{},[742,1442,757],{},[736,1444,1445,1448],{"accent":610},[599,1446,1447],{},"c",[742,1449,744],{},[742,1451,757],{},[736,1453,1454,1457],{"accent":610},[599,1455,1456],{},"d",[742,1458,744],{},[742,1460,808],{"stretchy":789},[603,1462,1463],{"encoding":605},"\\vec{s} = \\frac{1}{4}(\\vec{a} + \\vec{b} + \\vec{c} + \\vec{d})",[580,1465,1467,1518,1639,1690,1740],{"className":1466,"ariaHidden":610},[609],[580,1468,1470,1473,1509,1512,1515],{"className":1469},[614],[580,1471],{"className":1472,"style":821},[618],[580,1474,1476],{"className":1475},[623,825],[580,1477,1479],{"className":1478},[829],[580,1480,1482],{"className":1481},[833],[580,1483,1485,1493],{"className":1484,"style":821},[837],[580,1486,1487,1490],{"style":840},[580,1488],{"className":1489,"style":845},[844],[580,1491,1413],{"className":1492},[623,624],[580,1494,1495,1498],{"style":840},[580,1496],{"className":1497,"style":845},[844],[580,1499,1502],{"className":1500,"style":1501},[857],"left:-0.1799em;",[580,1503,1505],{"className":1504,"style":863},[862],[865,1506,1507],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,1508],{"d":876},[580,1510],{"className":1511,"style":881},[880],[580,1513,747],{"className":1514},[885],[580,1516],{"className":1517,"style":881},[880],[580,1519,1521,1524,1592,1595,1630,1633,1636],{"className":1520},[614],[580,1522],{"className":1523,"style":1098},[618],[580,1525,1527,1530,1589],{"className":1526},[623],[580,1528],{"className":1529},[955,956],[580,1531,1533],{"className":1532},[759],[580,1534,1536,1581],{"className":1535},[829,963],[580,1537,1539,1578],{"className":1538},[833],[580,1540,1542,1556,1564],{"className":1541,"style":970},[837],[580,1543,1544,1547],{"style":973},[580,1545],{"className":1546,"style":845},[844],[580,1548,1550],{"className":1549},[980,981,982,983],[580,1551,1553],{"className":1552},[623,983],[580,1554,1424],{"className":1555},[623,983],[580,1557,1558,1561],{"style":992},[580,1559],{"className":1560,"style":845},[844],[580,1562],{"className":1563,"style":1000},[999],[580,1565,1566,1569],{"style":1003},[580,1567],{"className":1568,"style":845},[844],[580,1570,1572],{"className":1571},[980,981,982,983],[580,1573,1575],{"className":1574},[623,983],[580,1576,764],{"className":1577},[623,983],[580,1579,1020],{"className":1580},[1019],[580,1582,1584],{"className":1583},[833],[580,1585,1587],{"className":1586,"style":1027},[837],[580,1588],{},[580,1590],{"className":1591},[1033,956],[580,1593,790],{"className":1594},[955],[580,1596,1598],{"className":1597},[623,825],[580,1599,1601],{"className":1600},[829],[580,1602,1604],{"className":1603},[833],[580,1605,1607,1615],{"className":1606,"style":821},[837],[580,1608,1609,1612],{"style":840},[580,1610],{"className":1611,"style":845},[844],[580,1613,752],{"className":1614},[623,624],[580,1616,1617,1620],{"style":840},[580,1618],{"className":1619,"style":845},[844],[580,1621,1623],{"className":1622,"style":858},[857],[580,1624,1626],{"className":1625,"style":863},[862],[865,1627,1628],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,1629],{"d":876},[580,1631],{"className":1632,"style":934},[880],[580,1634,757],{"className":1635},[938],[580,1637],{"className":1638,"style":934},[880],[580,1640,1642,1646,1681,1684,1687],{"className":1641},[614],[580,1643],{"className":1644,"style":1645},[618],"height:1.0608em;vertical-align:-0.0833em;",[580,1647,1649],{"className":1648},[623,825],[580,1650,1652],{"className":1651},[829],[580,1653,1655],{"className":1654},[833],[580,1656,1658,1666],{"className":1657,"style":1233},[837],[580,1659,1660,1663],{"style":840},[580,1661],{"className":1662,"style":845},[844],[580,1664,803],{"className":1665},[623,624],[580,1667,1668,1671],{"style":1244},[580,1669],{"className":1670,"style":845},[844],[580,1672,1674],{"className":1673,"style":858},[857],[580,1675,1677],{"className":1676,"style":863},[862],[865,1678,1679],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,1680],{"d":876},[580,1682],{"className":1683,"style":934},[880],[580,1685,757],{"className":1686},[938],[580,1688],{"className":1689,"style":934},[880],[580,1691,1693,1696,1731,1734,1737],{"className":1692},[614],[580,1694],{"className":1695,"style":895},[618],[580,1697,1699],{"className":1698},[623,825],[580,1700,1702],{"className":1701},[829],[580,1703,1705],{"className":1704},[833],[580,1706,1708,1716],{"className":1707,"style":821},[837],[580,1709,1710,1713],{"style":840},[580,1711],{"className":1712,"style":845},[844],[580,1714,1447],{"className":1715},[623,624],[580,1717,1718,1721],{"style":840},[580,1719],{"className":1720,"style":845},[844],[580,1722,1724],{"className":1723,"style":1501},[857],[580,1725,1727],{"className":1726,"style":863},[862],[865,1728,1729],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,1730],{"d":876},[580,1732],{"className":1733,"style":934},[880],[580,1735,757],{"className":1736},[938],[580,1738],{"className":1739,"style":934},[880],[580,1741,1743,1746,1782],{"className":1742},[614],[580,1744],{"className":1745,"style":1220},[618],[580,1747,1749],{"className":1748},[623,825],[580,1750,1752],{"className":1751},[829],[580,1753,1755],{"className":1754},[833],[580,1756,1758,1766],{"className":1757,"style":1233},[837],[580,1759,1760,1763],{"style":840},[580,1761],{"className":1762,"style":845},[844],[580,1764,1456],{"className":1765},[623,624],[580,1767,1768,1771],{"style":1244},[580,1769],{"className":1770,"style":845},[844],[580,1772,1775],{"className":1773,"style":1774},[857],"left:-0.0688em;",[580,1776,1778],{"className":1777,"style":863},[862],[865,1779,1780],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,1781],{"d":876},[580,1783,808],{"className":1784},[1033],[565,1786,1787],{},"Die Formeln gelten in der Ebene und im Raum. In der Ebene hat jeder Vektor nur zwei Komponenten.",[560,1789,1791],{"id":1790},"beispiele","Beispiele",[565,1793,1794,1885,1886,1356],{},[580,1795,1797,1827],{"className":1796},[583],[580,1798,1800],{"className":1799},[587],[589,1801,1802],{"xmlns":591},[593,1803,1804,1824],{},[596,1805,1806,1808,1810,1812,1815,1817,1819,1822],{},[599,1807,641],{},[742,1809,790],{"stretchy":789},[762,1811,764],{},[742,1813,1814],{},"∣",[762,1816,767],{},[742,1818,1814],{},[762,1820,1821],{},"3",[742,1823,808],{"stretchy":789},[603,1825,1826],{"encoding":605},"A(1 \\mid 2 \\mid 3)",[580,1828,1830,1855,1873],{"className":1829,"ariaHidden":610},[609],[580,1831,1833,1837,1840,1843,1846,1849,1852],{"className":1832},[614],[580,1834],{"className":1835,"style":1836},[618],"height:1em;vertical-align:-0.25em;",[580,1838,641],{"className":1839},[623,624],[580,1841,790],{"className":1842},[955],[580,1844,764],{"className":1845},[623],[580,1847],{"className":1848,"style":881},[880],[580,1850,1814],{"className":1851},[885],[580,1853],{"className":1854,"style":881},[880],[580,1856,1858,1861,1864,1867,1870],{"className":1857},[614],[580,1859],{"className":1860,"style":1836},[618],[580,1862,767],{"className":1863},[623],[580,1865],{"className":1866,"style":881},[880],[580,1868,1814],{"className":1869},[885],[580,1871],{"className":1872,"style":881},[880],[580,1874,1876,1879,1882],{"className":1875},[614],[580,1877],{"className":1878,"style":1836},[618],[580,1880,1821],{"className":1881},[623],[580,1883,808],{"className":1884},[1033]," und ",[580,1887,1889,1922],{"className":1888},[583],[580,1890,1892],{"className":1891},[587],[589,1893,1894],{"xmlns":591},[593,1895,1896,1919],{},[596,1897,1898,1900,1902,1905,1907,1910,1912,1915,1917],{},[599,1899,644],{},[742,1901,790],{"stretchy":789},[762,1903,1904],{},"5",[742,1906,1814],{},[762,1908,1909],{},"0",[742,1911,1814],{},[742,1913,1914],{},"−",[762,1916,764],{},[742,1918,808],{"stretchy":789},[603,1920,1921],{"encoding":605},"B(5 \\mid 0 \\mid -1)",[580,1923,1925,1949,1967],{"className":1924,"ariaHidden":610},[609],[580,1926,1928,1931,1934,1937,1940,1943,1946],{"className":1927},[614],[580,1929],{"className":1930,"style":1836},[618],[580,1932,644],{"className":1933,"style":663},[623,624],[580,1935,790],{"className":1936},[955],[580,1938,1904],{"className":1939},[623],[580,1941],{"className":1942,"style":881},[880],[580,1944,1814],{"className":1945},[885],[580,1947],{"className":1948,"style":881},[880],[580,1950,1952,1955,1958,1961,1964],{"className":1951},[614],[580,1953],{"className":1954,"style":1836},[618],[580,1956,1909],{"className":1957},[623],[580,1959],{"className":1960,"style":881},[880],[580,1962,1814],{"className":1963},[885],[580,1965],{"className":1966,"style":881},[880],[580,1968,1970,1973,1976,1979],{"className":1969},[614],[580,1971],{"className":1972,"style":1836},[618],[580,1974,1914],{"className":1975},[623],[580,1977,764],{"className":1978},[623],[580,1980,808],{"className":1981},[1033],[580,1983,1986],{"className":1984},[1985],"katex-display",[580,1987,1989,2113],{"className":1988},[583],[580,1990,1992],{"className":1991},[587],[589,1993,1995],{"xmlns":591,"display":1994},"block",[593,1996,1997,2110],{},[596,1998,1999,2005,2007,2013,2076,2078],{},[736,2000,2001,2003],{"accent":610},[599,2002,740],{},[742,2004,744],{},[742,2006,747],{},[759,2008,2009,2011],{},[762,2010,764],{},[762,2012,767],{},[596,2014,2015,2017,2074],{},[742,2016,790],{"fence":610},[2018,2019,2023,2040,2054],"mtable",{"rowspacing":2020,"columnalign":2021,"columnspacing":2022},"0.16em","center","1em",[2024,2025,2026],"mtr",{},[2027,2028,2029],"mtd",{},[2030,2031,2032],"mstyle",{"scriptlevel":1909,"displaystyle":789},[596,2033,2034,2036,2038],{},[762,2035,764],{},[742,2037,757],{},[762,2039,1904],{},[2024,2041,2042],{},[2027,2043,2044],{},[2030,2045,2046],{"scriptlevel":1909,"displaystyle":789},[596,2047,2048,2050,2052],{},[762,2049,767],{},[742,2051,757],{},[762,2053,1909],{},[2024,2055,2056],{},[2027,2057,2058],{},[2030,2059,2060],{"scriptlevel":1909,"displaystyle":789},[596,2061,2062,2064,2066,2068,2070,2072],{},[762,2063,1821],{},[742,2065,757],{},[742,2067,790],{"stretchy":789},[742,2069,1914],{},[762,2071,764],{},[742,2073,808],{"stretchy":789},[742,2075,808],{"fence":610},[742,2077,747],{},[596,2079,2080,2082,2108],{},[742,2081,790],{"fence":610},[2018,2083,2084,2092,2100],{"rowspacing":2020,"columnalign":2021,"columnspacing":2022},[2024,2085,2086],{},[2027,2087,2088],{},[2030,2089,2090],{"scriptlevel":1909,"displaystyle":789},[762,2091,1821],{},[2024,2093,2094],{},[2027,2095,2096],{},[2030,2097,2098],{"scriptlevel":1909,"displaystyle":789},[762,2099,764],{},[2024,2101,2102],{},[2027,2103,2104],{},[2030,2105,2106],{"scriptlevel":1909,"displaystyle":789},[762,2107,764],{},[742,2109,808],{"fence":610},[603,2111,2112],{"encoding":605},"\\vec{m} = \\frac{1}{2}\\begin{pmatrix} 1 + 5 \\\\ 2 + 0 \\\\ 3 + (-1) \\end{pmatrix} = \\begin{pmatrix} 3 \\\\ 1 \\\\ 1 \\end{pmatrix}",[580,2114,2116,2166,2453],{"className":2115,"ariaHidden":610},[609],[580,2117,2119,2122,2157,2160,2163],{"className":2118},[614],[580,2120],{"className":2121,"style":821},[618],[580,2123,2125],{"className":2124},[623,825],[580,2126,2128],{"className":2127},[829],[580,2129,2131],{"className":2130},[833],[580,2132,2134,2142],{"className":2133,"style":821},[837],[580,2135,2136,2139],{"style":840},[580,2137],{"className":2138,"style":845},[844],[580,2140,740],{"className":2141},[623,624],[580,2143,2144,2147],{"style":840},[580,2145],{"className":2146,"style":845},[844],[580,2148,2150],{"className":2149,"style":858},[857],[580,2151,2153],{"className":2152,"style":863},[862],[865,2154,2155],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,2156],{"d":876},[580,2158],{"className":2159,"style":881},[880],[580,2161,747],{"className":2162},[885],[580,2164],{"className":2165,"style":881},[880],[580,2167,2169,2173,2239,2243,2444,2447,2450],{"className":2168},[614],[580,2170],{"className":2171,"style":2172},[618],"height:3.6em;vertical-align:-1.55em;",[580,2174,2176,2179,2236],{"className":2175},[623],[580,2177],{"className":2178},[955,956],[580,2180,2182],{"className":2181},[759],[580,2183,2185,2227],{"className":2184},[829,963],[580,2186,2188,2224],{"className":2187},[833],[580,2189,2192,2204,2212],{"className":2190,"style":2191},[837],"height:1.3214em;",[580,2193,2195,2198],{"style":2194},"top:-2.314em;",[580,2196],{"className":2197,"style":845},[844],[580,2199,2201],{"className":2200},[623],[580,2202,767],{"className":2203},[623],[580,2205,2206,2209],{"style":992},[580,2207],{"className":2208,"style":845},[844],[580,2210],{"className":2211,"style":1000},[999],[580,2213,2215,2218],{"style":2214},"top:-3.677em;",[580,2216],{"className":2217,"style":845},[844],[580,2219,2221],{"className":2220},[623],[580,2222,764],{"className":2223},[623],[580,2225,1020],{"className":2226},[1019],[580,2228,2230],{"className":2229},[833],[580,2231,2234],{"className":2232,"style":2233},[837],"height:0.686em;",[580,2235],{},[580,2237],{"className":2238},[1033,956],[580,2240],{"className":2241,"style":2242},[880],"margin-right:0.1667em;",[580,2244,2247,2295,2406],{"className":2245},[2246],"minner",[580,2248,2250],{"className":2249},[955],[580,2251,2255],{"className":2252},[2253,2254],"delimsizing","mult",[580,2256,2258,2286],{"className":2257},[829,963],[580,2259,2261,2283],{"className":2260},[833],[580,2262,2265],{"className":2263,"style":2264},[837],"height:2.05em;",[580,2266,2268,2272],{"style":2267},"top:-4.05em;",[580,2269],{"className":2270,"style":2271},[844],"height:5.6em;",[580,2273,2275],{"style":2274},"width:0.875em;height:3.6em;",[865,2276,2280],{"xmlns":867,"width":2277,"height":2278,"viewBox":2279},"0.875em","3.6em","0 0 875 3600",[874,2281],{"d":2282},"M863,9c0,-2,-2,-5,-6,-9c0,0,-17,0,-17,0c-12.7,0,-19.3,0.3,-20,1\nc-5.3,5.3,-10.3,11,-15,17c-242.7,294.7,-395.3,682,-458,1162c-21.3,163.3,-33.3,349,\n-36,557 l0,84c0.2,6,0,26,0,60c2,159.3,10,310.7,24,454c53.3,528,210,\n949.7,470,1265c4.7,6,9.7,11.7,15,17c0.7,0.7,7,1,19,1c0,0,18,0,18,0c4,-4,6,-7,6,-9\nc0,-2.7,-3.3,-8.7,-10,-18c-135.3,-192.7,-235.5,-414.3,-300.5,-665c-65,-250.7,-102.5,\n-544.7,-112.5,-882c-2,-104,-3,-167,-3,-189\nl0,-92c0,-162.7,5.7,-314,17,-454c20.7,-272,63.7,-513,129,-723c65.3,\n-210,155.3,-396.3,270,-559c6.7,-9.3,10,-15.3,10,-18z",[580,2284,1020],{"className":2285},[1019],[580,2287,2289],{"className":2288},[833],[580,2290,2293],{"className":2291,"style":2292},[837],"height:1.55em;",[580,2294],{},[580,2296,2298],{"className":2297},[623],[580,2299,2301],{"className":2300},[2018],[580,2302,2305],{"className":2303},[2304],"col-align-c",[580,2306,2308,2398],{"className":2307},[829,963],[580,2309,2311,2395],{"className":2310},[833],[580,2312,2314,2338,2362],{"className":2313,"style":2264},[837],[580,2315,2317,2320],{"style":2316},"top:-4.21em;",[580,2318],{"className":2319,"style":845},[844],[580,2321,2323,2326,2329,2332,2335],{"className":2322},[623],[580,2324,764],{"className":2325},[623],[580,2327],{"className":2328,"style":934},[880],[580,2330,757],{"className":2331},[938],[580,2333],{"className":2334,"style":934},[880],[580,2336,1904],{"className":2337},[623],[580,2339,2341,2344],{"style":2340},"top:-3.01em;",[580,2342],{"className":2343,"style":845},[844],[580,2345,2347,2350,2353,2356,2359],{"className":2346},[623],[580,2348,767],{"className":2349},[623],[580,2351],{"className":2352,"style":934},[880],[580,2354,757],{"className":2355},[938],[580,2357],{"className":2358,"style":934},[880],[580,2360,1909],{"className":2361},[623],[580,2363,2365,2368],{"style":2364},"top:-1.81em;",[580,2366],{"className":2367,"style":845},[844],[580,2369,2371,2374,2377,2380,2383,2386,2389,2392],{"className":2370},[623],[580,2372,1821],{"className":2373},[623],[580,2375],{"className":2376,"style":934},[880],[580,2378,757],{"className":2379},[938],[580,2381],{"className":2382,"style":934},[880],[580,2384,790],{"className":2385},[955],[580,2387,1914],{"className":2388},[623],[580,2390,764],{"className":2391},[623],[580,2393,808],{"className":2394},[1033],[580,2396,1020],{"className":2397},[1019],[580,2399,2401],{"className":2400},[833],[580,2402,2404],{"className":2403,"style":2292},[837],[580,2405],{},[580,2407,2409],{"className":2408},[1033],[580,2410,2412],{"className":2411},[2253,2254],[580,2413,2415,2436],{"className":2414},[829,963],[580,2416,2418,2433],{"className":2417},[833],[580,2419,2421],{"className":2420,"style":2264},[837],[580,2422,2423,2426],{"style":2267},[580,2424],{"className":2425,"style":2271},[844],[580,2427,2428],{"style":2274},[865,2429,2430],{"xmlns":867,"width":2277,"height":2278,"viewBox":2279},[874,2431],{"d":2432},"M76,0c-16.7,0,-25,3,-25,9c0,2,2,6.3,6,13c21.3,28.7,42.3,60.3,\n63,95c96.7,156.7,172.8,332.5,228.5,527.5c55.7,195,92.8,416.5,111.5,664.5\nc11.3,139.3,17,290.7,17,454c0,28,1.7,43,3.3,45l0,9\nc-3,4,-3.3,16.7,-3.3,38c0,162,-5.7,313.7,-17,455c-18.7,248,-55.8,469.3,-111.5,664\nc-55.7,194.7,-131.8,370.3,-228.5,527c-20.7,34.7,-41.7,66.3,-63,95c-2,3.3,-4,7,-6,11\nc0,7.3,5.7,11,17,11c0,0,11,0,11,0c9.3,0,14.3,-0.3,15,-1c5.3,-5.3,10.3,-11,15,-17\nc242.7,-294.7,395.3,-681.7,458,-1161c21.3,-164.7,33.3,-350.7,36,-558\nl0,-144c-2,-159.3,-10,-310.7,-24,-454c-53.3,-528,-210,-949.7,\n-470,-1265c-4.7,-6,-9.7,-11.7,-15,-17c-0.7,-0.7,-6.7,-1,-18,-1z",[580,2434,1020],{"className":2435},[1019],[580,2437,2439],{"className":2438},[833],[580,2440,2442],{"className":2441,"style":2292},[837],[580,2443],{},[580,2445],{"className":2446,"style":881},[880],[580,2448,747],{"className":2449},[885],[580,2451],{"className":2452,"style":881},[880],[580,2454,2456,2459],{"className":2455},[614],[580,2457],{"className":2458,"style":2172},[618],[580,2460,2462,2499,2561],{"className":2461},[2246],[580,2463,2465],{"className":2464},[955],[580,2466,2468],{"className":2467},[2253,2254],[580,2469,2471,2491],{"className":2470},[829,963],[580,2472,2474,2488],{"className":2473},[833],[580,2475,2477],{"className":2476,"style":2264},[837],[580,2478,2479,2482],{"style":2267},[580,2480],{"className":2481,"style":2271},[844],[580,2483,2484],{"style":2274},[865,2485,2486],{"xmlns":867,"width":2277,"height":2278,"viewBox":2279},[874,2487],{"d":2282},[580,2489,1020],{"className":2490},[1019],[580,2492,2494],{"className":2493},[833],[580,2495,2497],{"className":2496,"style":2292},[837],[580,2498],{},[580,2500,2502],{"className":2501},[623],[580,2503,2505],{"className":2504},[2018],[580,2506,2508],{"className":2507},[2304],[580,2509,2511,2553],{"className":2510},[829,963],[580,2512,2514,2550],{"className":2513},[833],[580,2515,2517,2528,2539],{"className":2516,"style":2264},[837],[580,2518,2519,2522],{"style":2316},[580,2520],{"className":2521,"style":845},[844],[580,2523,2525],{"className":2524},[623],[580,2526,1821],{"className":2527},[623],[580,2529,2530,2533],{"style":2340},[580,2531],{"className":2532,"style":845},[844],[580,2534,2536],{"className":2535},[623],[580,2537,764],{"className":2538},[623],[580,2540,2541,2544],{"style":2364},[580,2542],{"className":2543,"style":845},[844],[580,2545,2547],{"className":2546},[623],[580,2548,764],{"className":2549},[623],[580,2551,1020],{"className":2552},[1019],[580,2554,2556],{"className":2555},[833],[580,2557,2559],{"className":2558,"style":2292},[837],[580,2560],{},[580,2562,2564],{"className":2563},[1033],[580,2565,2567],{"className":2566},[2253,2254],[580,2568,2570,2590],{"className":2569},[829,963],[580,2571,2573,2587],{"className":2572},[833],[580,2574,2576],{"className":2575,"style":2264},[837],[580,2577,2578,2581],{"style":2267},[580,2579],{"className":2580,"style":2271},[844],[580,2582,2583],{"style":2274},[865,2584,2585],{"xmlns":867,"width":2277,"height":2278,"viewBox":2279},[874,2586],{"d":2432},[580,2588,1020],{"className":2589},[1019],[580,2591,2593],{"className":2592},[833],[580,2594,2596],{"className":2595,"style":2292},[837],[580,2597],{},[565,2599,2600,2601,2689,2690,2728],{},"Mit ",[580,2602,2604,2632],{"className":2603},[583],[580,2605,2607],{"className":2606},[587],[589,2608,2609],{"xmlns":591},[593,2610,2611,2629],{},[596,2612,2613,2615,2617,2619,2621,2623,2625,2627],{},[599,2614,1316],{},[742,2616,790],{"stretchy":789},[762,2618,1909],{},[742,2620,1814],{},[762,2622,1424],{},[742,2624,1814],{},[762,2626,764],{},[742,2628,808],{"stretchy":789},[603,2630,2631],{"encoding":605},"C(0 \\mid 4 \\mid 1)",[580,2633,2635,2659,2677],{"className":2634,"ariaHidden":610},[609],[580,2636,2638,2641,2644,2647,2650,2653,2656],{"className":2637},[614],[580,2639],{"className":2640,"style":1836},[618],[580,2642,1316],{"className":2643,"style":1338},[623,624],[580,2645,790],{"className":2646},[955],[580,2648,1909],{"className":2649},[623],[580,2651],{"className":2652,"style":881},[880],[580,2654,1814],{"className":2655},[885],[580,2657],{"className":2658,"style":881},[880],[580,2660,2662,2665,2668,2671,2674],{"className":2661},[614],[580,2663],{"className":2664,"style":1836},[618],[580,2666,1424],{"className":2667},[623],[580,2669],{"className":2670,"style":881},[880],[580,2672,1814],{"className":2673},[885],[580,2675],{"className":2676,"style":881},[880],[580,2678,2680,2683,2686],{"className":2679},[614],[580,2681],{"className":2682,"style":1836},[618],[580,2684,764],{"className":2685},[623],[580,2687,808],{"className":2688},[1033]," hat das Dreieck ",[580,2691,2693,2710],{"className":2692},[583],[580,2694,2696],{"className":2695},[587],[589,2697,2698],{"xmlns":591},[593,2699,2700,2708],{},[596,2701,2702,2704,2706],{},[599,2703,641],{},[599,2705,644],{},[599,2707,1316],{},[603,2709,1319],{"encoding":605},[580,2711,2713],{"className":2712,"ariaHidden":610},[609],[580,2714,2716,2719,2722,2725],{"className":2715},[614],[580,2717],{"className":2718,"style":619},[618],[580,2720,641],{"className":2721},[623,624],[580,2723,644],{"className":2724,"style":663},[623,624],[580,2726,1316],{"className":2727,"style":1338},[623,624]," den Schwerpunkt",[580,2730,2732],{"className":2731},[1985],[580,2733,2735,2857],{"className":2734},[583],[580,2736,2738],{"className":2737},[587],[589,2739,2740],{"xmlns":591,"display":1994},[593,2741,2742,2854],{},[596,2743,2744,2750,2752,2758,2820,2822],{},[736,2745,2746,2748],{"accent":610},[599,2747,1413],{},[742,2749,744],{},[742,2751,747],{},[759,2753,2754,2756],{},[762,2755,764],{},[762,2757,1821],{},[596,2759,2760,2762,2818],{},[742,2761,790],{"fence":610},[2018,2763,2764,2782,2800],{"rowspacing":2020,"columnalign":2021,"columnspacing":2022},[2024,2765,2766],{},[2027,2767,2768],{},[2030,2769,2770],{"scriptlevel":1909,"displaystyle":789},[596,2771,2772,2774,2776,2778,2780],{},[762,2773,764],{},[742,2775,757],{},[762,2777,1904],{},[742,2779,757],{},[762,2781,1909],{},[2024,2783,2784],{},[2027,2785,2786],{},[2030,2787,2788],{"scriptlevel":1909,"displaystyle":789},[596,2789,2790,2792,2794,2796,2798],{},[762,2791,767],{},[742,2793,757],{},[762,2795,1909],{},[742,2797,757],{},[762,2799,1424],{},[2024,2801,2802],{},[2027,2803,2804],{},[2030,2805,2806],{"scriptlevel":1909,"displaystyle":789},[596,2807,2808,2810,2812,2814,2816],{},[762,2809,1821],{},[742,2811,1914],{},[762,2813,764],{},[742,2815,757],{},[762,2817,764],{},[742,2819,808],{"fence":610},[742,2821,747],{},[596,2823,2824,2826,2852],{},[742,2825,790],{"fence":610},[2018,2827,2828,2836,2844],{"rowspacing":2020,"columnalign":2021,"columnspacing":2022},[2024,2829,2830],{},[2027,2831,2832],{},[2030,2833,2834],{"scriptlevel":1909,"displaystyle":789},[762,2835,767],{},[2024,2837,2838],{},[2027,2839,2840],{},[2030,2841,2842],{"scriptlevel":1909,"displaystyle":789},[762,2843,767],{},[2024,2845,2846],{},[2027,2847,2848],{},[2030,2849,2850],{"scriptlevel":1909,"displaystyle":789},[762,2851,764],{},[742,2853,808],{"fence":610},[603,2855,2856],{"encoding":605},"\\vec{s} = \\frac{1}{3}\\begin{pmatrix} 1 + 5 + 0 \\\\ 2 + 0 + 4 \\\\ 3 - 1 + 1 \\end{pmatrix} = \\begin{pmatrix} 2 \\\\ 2 \\\\ 1 \\end{pmatrix}",[580,2858,2860,2910,3201],{"className":2859,"ariaHidden":610},[609],[580,2861,2863,2866,2901,2904,2907],{"className":2862},[614],[580,2864],{"className":2865,"style":821},[618],[580,2867,2869],{"className":2868},[623,825],[580,2870,2872],{"className":2871},[829],[580,2873,2875],{"className":2874},[833],[580,2876,2878,2886],{"className":2877,"style":821},[837],[580,2879,2880,2883],{"style":840},[580,2881],{"className":2882,"style":845},[844],[580,2884,1413],{"className":2885},[623,624],[580,2887,2888,2891],{"style":840},[580,2889],{"className":2890,"style":845},[844],[580,2892,2894],{"className":2893,"style":1501},[857],[580,2895,2897],{"className":2896,"style":863},[862],[865,2898,2899],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,2900],{"d":876},[580,2902],{"className":2903,"style":881},[880],[580,2905,747],{"className":2906},[885],[580,2908],{"className":2909,"style":881},[880],[580,2911,2913,2916,2978,2981,3192,3195,3198],{"className":2912},[614],[580,2914],{"className":2915,"style":2172},[618],[580,2917,2919,2922,2975],{"className":2918},[623],[580,2920],{"className":2921},[955,956],[580,2923,2925],{"className":2924},[759],[580,2926,2928,2967],{"className":2927},[829,963],[580,2929,2931,2964],{"className":2930},[833],[580,2932,2934,2945,2953],{"className":2933,"style":2191},[837],[580,2935,2936,2939],{"style":2194},[580,2937],{"className":2938,"style":845},[844],[580,2940,2942],{"className":2941},[623],[580,2943,1821],{"className":2944},[623],[580,2946,2947,2950],{"style":992},[580,2948],{"className":2949,"style":845},[844],[580,2951],{"className":2952,"style":1000},[999],[580,2954,2955,2958],{"style":2214},[580,2956],{"className":2957,"style":845},[844],[580,2959,2961],{"className":2960},[623],[580,2962,764],{"className":2963},[623],[580,2965,1020],{"className":2966},[1019],[580,2968,2970],{"className":2969},[833],[580,2971,2973],{"className":2972,"style":2233},[837],[580,2974],{},[580,2976],{"className":2977},[1033,956],[580,2979],{"className":2980,"style":2242},[880],[580,2982,2984,3021,3155],{"className":2983},[2246],[580,2985,2987],{"className":2986},[955],[580,2988,2990],{"className":2989},[2253,2254],[580,2991,2993,3013],{"className":2992},[829,963],[580,2994,2996,3010],{"className":2995},[833],[580,2997,2999],{"className":2998,"style":2264},[837],[580,3000,3001,3004],{"style":2267},[580,3002],{"className":3003,"style":2271},[844],[580,3005,3006],{"style":2274},[865,3007,3008],{"xmlns":867,"width":2277,"height":2278,"viewBox":2279},[874,3009],{"d":2282},[580,3011,1020],{"className":3012},[1019],[580,3014,3016],{"className":3015},[833],[580,3017,3019],{"className":3018,"style":2292},[837],[580,3020],{},[580,3022,3024],{"className":3023},[623],[580,3025,3027],{"className":3026},[2018],[580,3028,3030],{"className":3029},[2304],[580,3031,3033,3147],{"className":3032},[829,963],[580,3034,3036,3144],{"className":3035},[833],[580,3037,3039,3074,3109],{"className":3038,"style":2264},[837],[580,3040,3041,3044],{"style":2316},[580,3042],{"className":3043,"style":845},[844],[580,3045,3047,3050,3053,3056,3059,3062,3065,3068,3071],{"className":3046},[623],[580,3048,764],{"className":3049},[623],[580,3051],{"className":3052,"style":934},[880],[580,3054,757],{"className":3055},[938],[580,3057],{"className":3058,"style":934},[880],[580,3060,1904],{"className":3061},[623],[580,3063],{"className":3064,"style":934},[880],[580,3066,757],{"className":3067},[938],[580,3069],{"className":3070,"style":934},[880],[580,3072,1909],{"className":3073},[623],[580,3075,3076,3079],{"style":2340},[580,3077],{"className":3078,"style":845},[844],[580,3080,3082,3085,3088,3091,3094,3097,3100,3103,3106],{"className":3081},[623],[580,3083,767],{"className":3084},[623],[580,3086],{"className":3087,"style":934},[880],[580,3089,757],{"className":3090},[938],[580,3092],{"className":3093,"style":934},[880],[580,3095,1909],{"className":3096},[623],[580,3098],{"className":3099,"style":934},[880],[580,3101,757],{"className":3102},[938],[580,3104],{"className":3105,"style":934},[880],[580,3107,1424],{"className":3108},[623],[580,3110,3111,3114],{"style":2364},[580,3112],{"className":3113,"style":845},[844],[580,3115,3117,3120,3123,3126,3129,3132,3135,3138,3141],{"className":3116},[623],[580,3118,1821],{"className":3119},[623],[580,3121],{"className":3122,"style":934},[880],[580,3124,1914],{"className":3125},[938],[580,3127],{"className":3128,"style":934},[880],[580,3130,764],{"className":3131},[623],[580,3133],{"className":3134,"style":934},[880],[580,3136,757],{"className":3137},[938],[580,3139],{"className":3140,"style":934},[880],[580,3142,764],{"className":3143},[623],[580,3145,1020],{"className":3146},[1019],[580,3148,3150],{"className":3149},[833],[580,3151,3153],{"className":3152,"style":2292},[837],[580,3154],{},[580,3156,3158],{"className":3157},[1033],[580,3159,3161],{"className":3160},[2253,2254],[580,3162,3164,3184],{"className":3163},[829,963],[580,3165,3167,3181],{"className":3166},[833],[580,3168,3170],{"className":3169,"style":2264},[837],[580,3171,3172,3175],{"style":2267},[580,3173],{"className":3174,"style":2271},[844],[580,3176,3177],{"style":2274},[865,3178,3179],{"xmlns":867,"width":2277,"height":2278,"viewBox":2279},[874,3180],{"d":2432},[580,3182,1020],{"className":3183},[1019],[580,3185,3187],{"className":3186},[833],[580,3188,3190],{"className":3189,"style":2292},[837],[580,3191],{},[580,3193],{"className":3194,"style":881},[880],[580,3196,747],{"className":3197},[885],[580,3199],{"className":3200,"style":881},[880],[580,3202,3204,3207],{"className":3203},[614],[580,3205],{"className":3206,"style":2172},[618],[580,3208,3210,3247,3309],{"className":3209},[2246],[580,3211,3213],{"className":3212},[955],[580,3214,3216],{"className":3215},[2253,2254],[580,3217,3219,3239],{"className":3218},[829,963],[580,3220,3222,3236],{"className":3221},[833],[580,3223,3225],{"className":3224,"style":2264},[837],[580,3226,3227,3230],{"style":2267},[580,3228],{"className":3229,"style":2271},[844],[580,3231,3232],{"style":2274},[865,3233,3234],{"xmlns":867,"width":2277,"height":2278,"viewBox":2279},[874,3235],{"d":2282},[580,3237,1020],{"className":3238},[1019],[580,3240,3242],{"className":3241},[833],[580,3243,3245],{"className":3244,"style":2292},[837],[580,3246],{},[580,3248,3250],{"className":3249},[623],[580,3251,3253],{"className":3252},[2018],[580,3254,3256],{"className":3255},[2304],[580,3257,3259,3301],{"className":3258},[829,963],[580,3260,3262,3298],{"className":3261},[833],[580,3263,3265,3276,3287],{"className":3264,"style":2264},[837],[580,3266,3267,3270],{"style":2316},[580,3268],{"className":3269,"style":845},[844],[580,3271,3273],{"className":3272},[623],[580,3274,767],{"className":3275},[623],[580,3277,3278,3281],{"style":2340},[580,3279],{"className":3280,"style":845},[844],[580,3282,3284],{"className":3283},[623],[580,3285,767],{"className":3286},[623],[580,3288,3289,3292],{"style":2364},[580,3290],{"className":3291,"style":845},[844],[580,3293,3295],{"className":3294},[623],[580,3296,764],{"className":3297},[623],[580,3299,1020],{"className":3300},[1019],[580,3302,3304],{"className":3303},[833],[580,3305,3307],{"className":3306,"style":2292},[837],[580,3308],{},[580,3310,3312],{"className":3311},[1033],[580,3313,3315],{"className":3314},[2253,2254],[580,3316,3318,3338],{"className":3317},[829,963],[580,3319,3321,3335],{"className":3320},[833],[580,3322,3324],{"className":3323,"style":2264},[837],[580,3325,3326,3329],{"style":2267},[580,3327],{"className":3328,"style":2271},[844],[580,3330,3331],{"style":2274},[865,3332,3333],{"xmlns":867,"width":2277,"height":2278,"viewBox":2279},[874,3334],{"d":2432},[580,3336,1020],{"className":3337},[1019],[580,3339,3341],{"className":3340},[833],[580,3342,3344],{"className":3343,"style":2292},[837],[580,3345],{},[565,3347,3348,3349,3383,3384,3479,3480,3508,3509,1261],{},"Kontrolle über die Seitenhalbierende: Die Mitte von ",[580,3350,3352,3368],{"className":3351},[583],[580,3353,3355],{"className":3354},[587],[589,3356,3357],{"xmlns":591},[593,3358,3359,3365],{},[596,3360,3361,3363],{},[599,3362,644],{},[599,3364,1316],{},[603,3366,3367],{"encoding":605},"BC",[580,3369,3371],{"className":3370,"ariaHidden":610},[609],[580,3372,3374,3377,3380],{"className":3373},[614],[580,3375],{"className":3376,"style":619},[618],[580,3378,644],{"className":3379,"style":663},[623,624],[580,3381,1316],{"className":3382,"style":1338},[623,624]," ist ",[580,3385,3387,3414],{"className":3386},[583],[580,3388,3390],{"className":3389},[587],[589,3391,3392],{"xmlns":591},[593,3393,3394,3411],{},[596,3395,3396,3398,3401,3403,3405,3407,3409],{},[742,3397,790],{"stretchy":789},[762,3399,3400],{},"2,5",[742,3402,1814],{},[762,3404,767],{},[742,3406,1814],{},[762,3408,1909],{},[742,3410,808],{"stretchy":789},[603,3412,3413],{"encoding":605},"(2{,}5 \\mid 2 \\mid 0)",[580,3415,3417,3449,3467],{"className":3416,"ariaHidden":610},[609],[580,3418,3420,3423,3426,3429,3437,3440,3443,3446],{"className":3419},[614],[580,3421],{"className":3422,"style":1836},[618],[580,3424,790],{"className":3425},[955],[580,3427,767],{"className":3428},[623],[580,3430,3432],{"className":3431},[623],[580,3433,3436],{"className":3434},[3435],"mpunct",",",[580,3438,1904],{"className":3439},[623],[580,3441],{"className":3442,"style":881},[880],[580,3444,1814],{"className":3445},[885],[580,3447],{"className":3448,"style":881},[880],[580,3450,3452,3455,3458,3461,3464],{"className":3451},[614],[580,3453],{"className":3454,"style":1836},[618],[580,3456,767],{"className":3457},[623],[580,3459],{"className":3460,"style":881},[880],[580,3462,1814],{"className":3463},[885],[580,3465],{"className":3466,"style":881},[880],[580,3468,3470,3473,3476],{"className":3469},[614],[580,3471],{"className":3472,"style":1836},[618],[580,3474,1909],{"className":3475},[623],[580,3477,808],{"className":3478},[1033],". Zwei Drittel des Wegs von ",[580,3481,3483,3496],{"className":3482},[583],[580,3484,3486],{"className":3485},[587],[589,3487,3488],{"xmlns":591},[593,3489,3490,3494],{},[596,3491,3492],{},[599,3493,641],{},[603,3495,641],{"encoding":605},[580,3497,3499],{"className":3498,"ariaHidden":610},[609],[580,3500,3502,3505],{"className":3501},[614],[580,3503],{"className":3504,"style":619},[618],[580,3506,641],{"className":3507},[623,624]," dorthin führen zu ",[580,3510,3512,3586],{"className":3511},[583],[580,3513,3515],{"className":3514},[587],[589,3516,3517],{"xmlns":591},[593,3518,3519,3583],{},[596,3520,3521,3523,3525,3527,3533,3536,3539,3541,3543,3545,3547,3549,3555,3557,3559,3561,3563,3565,3567,3569,3571,3573,3575,3577,3579,3581],{},[742,3522,790],{"stretchy":789},[762,3524,764],{},[742,3526,757],{},[759,3528,3529,3531],{},[762,3530,767],{},[762,3532,1821],{},[742,3534,3535],{},"⋅",[762,3537,3538],{},"1,5",[742,3540,1814],{},[762,3542,767],{},[742,3544,1814],{},[762,3546,1821],{},[742,3548,757],{},[759,3550,3551,3553],{},[762,3552,767],{},[762,3554,1821],{},[742,3556,3535],{},[742,3558,790],{"stretchy":789},[742,3560,1914],{},[762,3562,1821],{},[742,3564,808],{"stretchy":789},[742,3566,808],{"stretchy":789},[742,3568,747],{},[742,3570,790],{"stretchy":789},[762,3572,767],{},[742,3574,1814],{},[762,3576,767],{},[742,3578,1814],{},[762,3580,764],{},[742,3582,808],{"stretchy":789},[603,3584,3585],{"encoding":605},"(1 + \\frac{2}{3} \\cdot 1{,}5 \\mid 2 \\mid 3 + \\frac{2}{3} \\cdot (-3)) = (2 \\mid 2 \\mid 1)",[580,3587,3589,3610,3693,3720,3738,3757,3840,3868,3889,3907],{"className":3588,"ariaHidden":610},[609],[580,3590,3592,3595,3598,3601,3604,3607],{"className":3591},[614],[580,3593],{"className":3594,"style":1836},[618],[580,3596,790],{"className":3597},[955],[580,3599,764],{"className":3600},[623],[580,3602],{"className":3603,"style":934},[880],[580,3605,757],{"className":3606},[938],[580,3608],{"className":3609,"style":934},[880],[580,3611,3613,3616,3684,3687,3690],{"className":3612},[614],[580,3614],{"className":3615,"style":1098},[618],[580,3617,3619,3622,3681],{"className":3618},[623],[580,3620],{"className":3621},[955,956],[580,3623,3625],{"className":3624},[759],[580,3626,3628,3673],{"className":3627},[829,963],[580,3629,3631,3670],{"className":3630},[833],[580,3632,3634,3648,3656],{"className":3633,"style":970},[837],[580,3635,3636,3639],{"style":973},[580,3637],{"className":3638,"style":845},[844],[580,3640,3642],{"className":3641},[980,981,982,983],[580,3643,3645],{"className":3644},[623,983],[580,3646,1821],{"className":3647},[623,983],[580,3649,3650,3653],{"style":992},[580,3651],{"className":3652,"style":845},[844],[580,3654],{"className":3655,"style":1000},[999],[580,3657,3658,3661],{"style":1003},[580,3659],{"className":3660,"style":845},[844],[580,3662,3664],{"className":3663},[980,981,982,983],[580,3665,3667],{"className":3666},[623,983],[580,3668,767],{"className":3669},[623,983],[580,3671,1020],{"className":3672},[1019],[580,3674,3676],{"className":3675},[833],[580,3677,3679],{"className":3678,"style":1027},[837],[580,3680],{},[580,3682],{"className":3683},[1033,956],[580,3685],{"className":3686,"style":934},[880],[580,3688,3535],{"className":3689},[938],[580,3691],{"className":3692,"style":934},[880],[580,3694,3696,3699,3702,3708,3711,3714,3717],{"className":3695},[614],[580,3697],{"className":3698,"style":1836},[618],[580,3700,764],{"className":3701},[623],[580,3703,3705],{"className":3704},[623],[580,3706,3436],{"className":3707},[3435],[580,3709,1904],{"className":3710},[623],[580,3712],{"className":3713,"style":881},[880],[580,3715,1814],{"className":3716},[885],[580,3718],{"className":3719,"style":881},[880],[580,3721,3723,3726,3729,3732,3735],{"className":3722},[614],[580,3724],{"className":3725,"style":1836},[618],[580,3727,767],{"className":3728},[623],[580,3730],{"className":3731,"style":881},[880],[580,3733,1814],{"className":3734},[885],[580,3736],{"className":3737,"style":881},[880],[580,3739,3741,3745,3748,3751,3754],{"className":3740},[614],[580,3742],{"className":3743,"style":3744},[618],"height:0.7278em;vertical-align:-0.0833em;",[580,3746,1821],{"className":3747},[623],[580,3749],{"className":3750,"style":934},[880],[580,3752,757],{"className":3753},[938],[580,3755],{"className":3756,"style":934},[880],[580,3758,3760,3763,3831,3834,3837],{"className":3759},[614],[580,3761],{"className":3762,"style":1098},[618],[580,3764,3766,3769,3828],{"className":3765},[623],[580,3767],{"className":3768},[955,956],[580,3770,3772],{"className":3771},[759],[580,3773,3775,3820],{"className":3774},[829,963],[580,3776,3778,3817],{"className":3777},[833],[580,3779,3781,3795,3803],{"className":3780,"style":970},[837],[580,3782,3783,3786],{"style":973},[580,3784],{"className":3785,"style":845},[844],[580,3787,3789],{"className":3788},[980,981,982,983],[580,3790,3792],{"className":3791},[623,983],[580,3793,1821],{"className":3794},[623,983],[580,3796,3797,3800],{"style":992},[580,3798],{"className":3799,"style":845},[844],[580,3801],{"className":3802,"style":1000},[999],[580,3804,3805,3808],{"style":1003},[580,3806],{"className":3807,"style":845},[844],[580,3809,3811],{"className":3810},[980,981,982,983],[580,3812,3814],{"className":3813},[623,983],[580,3815,767],{"className":3816},[623,983],[580,3818,1020],{"className":3819},[1019],[580,3821,3823],{"className":3822},[833],[580,3824,3826],{"className":3825,"style":1027},[837],[580,3827],{},[580,3829],{"className":3830},[1033,956],[580,3832],{"className":3833,"style":934},[880],[580,3835,3535],{"className":3836},[938],[580,3838],{"className":3839,"style":934},[880],[580,3841,3843,3846,3849,3852,3855,3859,3862,3865],{"className":3842},[614],[580,3844],{"className":3845,"style":1836},[618],[580,3847,790],{"className":3848},[955],[580,3850,1914],{"className":3851},[623],[580,3853,1821],{"className":3854},[623],[580,3856,3858],{"className":3857},[1033],"))",[580,3860],{"className":3861,"style":881},[880],[580,3863,747],{"className":3864},[885],[580,3866],{"className":3867,"style":881},[880],[580,3869,3871,3874,3877,3880,3883,3886],{"className":3870},[614],[580,3872],{"className":3873,"style":1836},[618],[580,3875,790],{"className":3876},[955],[580,3878,767],{"className":3879},[623],[580,3881],{"className":3882,"style":881},[880],[580,3884,1814],{"className":3885},[885],[580,3887],{"className":3888,"style":881},[880],[580,3890,3892,3895,3898,3901,3904],{"className":3891},[614],[580,3893],{"className":3894,"style":1836},[618],[580,3896,767],{"className":3897},[623],[580,3899],{"className":3900,"style":881},[880],[580,3902,1814],{"className":3903},[885],[580,3905],{"className":3906,"style":881},[880],[580,3908,3910,3913,3916],{"className":3909},[614],[580,3911],{"className":3912,"style":1836},[618],[580,3914,764],{"className":3915},[623],[580,3917,808],{"className":3918},[1033],[565,3920,3921,3922,3968,3969,4332,4333,4427,4428,1261],{},"Vierter Eckpunkt des Parallelogramms ",[580,3923,3925,3946],{"className":3924},[583],[580,3926,3928],{"className":3927},[587],[589,3929,3930],{"xmlns":591},[593,3931,3932,3943],{},[596,3933,3934,3936,3938,3940],{},[599,3935,641],{},[599,3937,644],{},[599,3939,1316],{},[599,3941,3942],{},"D",[603,3944,3945],{"encoding":605},"ABCD",[580,3947,3949],{"className":3948,"ariaHidden":610},[609],[580,3950,3952,3955,3958,3961,3964],{"className":3951},[614],[580,3953],{"className":3954,"style":619},[618],[580,3956,641],{"className":3957},[623,624],[580,3959,644],{"className":3960,"style":663},[623,624],[580,3962,1316],{"className":3963,"style":1338},[623,624],[580,3965,3942],{"className":3966,"style":3967},[623,624],"margin-right:0.0278em;",": ",[580,3970,3972,4034],{"className":3971},[583],[580,3973,3975],{"className":3974},[587],[589,3976,3977],{"xmlns":591},[593,3978,3979,4031],{},[596,3980,3981,3987,3989,3995,3997,4007,4009,4015,4017,4023,4025],{},[736,3982,3983,3985],{"accent":610},[599,3984,1456],{},[742,3986,744],{},[742,3988,747],{},[736,3990,3991,3993],{"accent":610},[599,3992,752],{},[742,3994,744],{},[742,3996,757],{},[736,3998,3999,4005],{"accent":610},[596,4000,4001,4003],{},[599,4002,644],{},[599,4004,1316],{},[742,4006,778],{"stretchy":610},[742,4008,747],{},[736,4010,4011,4013],{"accent":610},[599,4012,752],{},[742,4014,744],{},[742,4016,757],{},[736,4018,4019,4021],{"accent":610},[599,4020,1447],{},[742,4022,744],{},[742,4024,1914],{},[736,4026,4027,4029],{"accent":610},[599,4028,803],{},[742,4030,744],{},[603,4032,4033],{"encoding":605},"\\vec{d} = \\vec{a} + \\overrightarrow{BC} = \\vec{a} + \\vec{c} - \\vec{b}",[580,4035,4037,4087,4137,4191,4241,4291],{"className":4036,"ariaHidden":610},[609],[580,4038,4040,4043,4078,4081,4084],{"className":4039},[614],[580,4041],{"className":4042,"style":1233},[618],[580,4044,4046],{"className":4045},[623,825],[580,4047,4049],{"className":4048},[829],[580,4050,4052],{"className":4051},[833],[580,4053,4055,4063],{"className":4054,"style":1233},[837],[580,4056,4057,4060],{"style":840},[580,4058],{"className":4059,"style":845},[844],[580,4061,1456],{"className":4062},[623,624],[580,4064,4065,4068],{"style":1244},[580,4066],{"className":4067,"style":845},[844],[580,4069,4071],{"className":4070,"style":1774},[857],[580,4072,4074],{"className":4073,"style":863},[862],[865,4075,4076],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,4077],{"d":876},[580,4079],{"className":4080,"style":881},[880],[580,4082,747],{"className":4083},[885],[580,4085],{"className":4086,"style":881},[880],[580,4088,4090,4093,4128,4131,4134],{"className":4089},[614],[580,4091],{"className":4092,"style":895},[618],[580,4094,4096],{"className":4095},[623,825],[580,4097,4099],{"className":4098},[829],[580,4100,4102],{"className":4101},[833],[580,4103,4105,4113],{"className":4104,"style":821},[837],[580,4106,4107,4110],{"style":840},[580,4108],{"className":4109,"style":845},[844],[580,4111,752],{"className":4112},[623,624],[580,4114,4115,4118],{"style":840},[580,4116],{"className":4117,"style":845},[844],[580,4119,4121],{"className":4120,"style":858},[857],[580,4122,4124],{"className":4123,"style":863},[862],[865,4125,4126],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,4127],{"d":876},[580,4129],{"className":4130,"style":934},[880],[580,4132,757],{"className":4133},[938],[580,4135],{"className":4136,"style":934},[880],[580,4138,4140,4143,4182,4185,4188],{"className":4139},[614],[580,4141],{"className":4142,"style":1046},[618],[580,4144,4146],{"className":4145},[623,825],[580,4147,4149],{"className":4148},[829],[580,4150,4152],{"className":4151},[833],[580,4153,4155,4169],{"className":4154,"style":1046},[837],[580,4156,4157,4160],{"style":840},[580,4158],{"className":4159,"style":845},[844],[580,4161,4163,4166],{"className":4162},[623],[580,4164,644],{"className":4165,"style":663},[623,624],[580,4167,1316],{"className":4168,"style":1338},[623,624],[580,4170,4172,4175],{"className":4171,"style":1065},[1064],[580,4173],{"className":4174,"style":845},[844],[580,4176,4178],{"className":4177,"style":1073},[1072],[865,4179,4180],{"xmlns":867,"width":1076,"height":1077,"viewBox":1078,"preserveAspectRatio":1079},[874,4181],{"d":1082},[580,4183],{"className":4184,"style":881},[880],[580,4186,747],{"className":4187},[885],[580,4189],{"className":4190,"style":881},[880],[580,4192,4194,4197,4232,4235,4238],{"className":4193},[614],[580,4195],{"className":4196,"style":895},[618],[580,4198,4200],{"className":4199},[623,825],[580,4201,4203],{"className":4202},[829],[580,4204,4206],{"className":4205},[833],[580,4207,4209,4217],{"className":4208,"style":821},[837],[580,4210,4211,4214],{"style":840},[580,4212],{"className":4213,"style":845},[844],[580,4215,752],{"className":4216},[623,624],[580,4218,4219,4222],{"style":840},[580,4220],{"className":4221,"style":845},[844],[580,4223,4225],{"className":4224,"style":858},[857],[580,4226,4228],{"className":4227,"style":863},[862],[865,4229,4230],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,4231],{"d":876},[580,4233],{"className":4234,"style":934},[880],[580,4236,757],{"className":4237},[938],[580,4239],{"className":4240,"style":934},[880],[580,4242,4244,4247,4282,4285,4288],{"className":4243},[614],[580,4245],{"className":4246,"style":895},[618],[580,4248,4250],{"className":4249},[623,825],[580,4251,4253],{"className":4252},[829],[580,4254,4256],{"className":4255},[833],[580,4257,4259,4267],{"className":4258,"style":821},[837],[580,4260,4261,4264],{"style":840},[580,4262],{"className":4263,"style":845},[844],[580,4265,1447],{"className":4266},[623,624],[580,4268,4269,4272],{"style":840},[580,4270],{"className":4271,"style":845},[844],[580,4273,4275],{"className":4274,"style":1501},[857],[580,4276,4278],{"className":4277,"style":863},[862],[865,4279,4280],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,4281],{"d":876},[580,4283],{"className":4284,"style":934},[880],[580,4286,1914],{"className":4287},[938],[580,4289],{"className":4290,"style":934},[880],[580,4292,4294,4297],{"className":4293},[614],[580,4295],{"className":4296,"style":1233},[618],[580,4298,4300],{"className":4299},[623,825],[580,4301,4303],{"className":4302},[829],[580,4304,4306],{"className":4305},[833],[580,4307,4309,4317],{"className":4308,"style":1233},[837],[580,4310,4311,4314],{"style":840},[580,4312],{"className":4313,"style":845},[844],[580,4315,803],{"className":4316},[623,624],[580,4318,4319,4322],{"style":1244},[580,4320],{"className":4321,"style":845},[844],[580,4323,4325],{"className":4324,"style":858},[857],[580,4326,4328],{"className":4327,"style":863},[862],[865,4329,4330],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,4331],{"d":876},", also ",[580,4334,4336,4367],{"className":4335},[583],[580,4337,4339],{"className":4338},[587],[589,4340,4341],{"xmlns":591},[593,4342,4343,4364],{},[596,4344,4345,4347,4349,4351,4353,4355,4358,4360,4362],{},[599,4346,3942],{},[742,4348,790],{"stretchy":789},[742,4350,1914],{},[762,4352,1424],{},[742,4354,1814],{},[762,4356,4357],{},"6",[742,4359,1814],{},[762,4361,1904],{},[742,4363,808],{"stretchy":789},[603,4365,4366],{"encoding":605},"D(-4 \\mid 6 \\mid 5)",[580,4368,4370,4397,4415],{"className":4369,"ariaHidden":610},[609],[580,4371,4373,4376,4379,4382,4385,4388,4391,4394],{"className":4372},[614],[580,4374],{"className":4375,"style":1836},[618],[580,4377,3942],{"className":4378,"style":3967},[623,624],[580,4380,790],{"className":4381},[955],[580,4383,1914],{"className":4384},[623],[580,4386,1424],{"className":4387},[623],[580,4389],{"className":4390,"style":881},[880],[580,4392,1814],{"className":4393},[885],[580,4395],{"className":4396,"style":881},[880],[580,4398,4400,4403,4406,4409,4412],{"className":4399},[614],[580,4401],{"className":4402,"style":1836},[618],[580,4404,4357],{"className":4405},[623],[580,4407],{"className":4408,"style":881},[880],[580,4410,1814],{"className":4411},[885],[580,4413],{"className":4414,"style":881},[880],[580,4416,4418,4421,4424],{"className":4417},[614],[580,4419],{"className":4420,"style":1836},[618],[580,4422,1904],{"className":4423},[623],[580,4425,808],{"className":4426},[1033],". Die Diagonalen halbieren sich, beide haben den Mittelpunkt ",[580,4429,4431,4458],{"className":4430},[583],[580,4432,4434],{"className":4433},[587],[589,4435,4436],{"xmlns":591},[593,4437,4438,4455],{},[596,4439,4440,4442,4445,4447,4449,4451,4453],{},[742,4441,790],{"stretchy":789},[762,4443,4444],{},"0,5",[742,4446,1814],{},[762,4448,1821],{},[742,4450,1814],{},[762,4452,767],{},[742,4454,808],{"stretchy":789},[603,4456,4457],{"encoding":605},"(0{,}5 \\mid 3 \\mid 2)",[580,4459,4461,4491,4509],{"className":4460,"ariaHidden":610},[609],[580,4462,4464,4467,4470,4473,4479,4482,4485,4488],{"className":4463},[614],[580,4465],{"className":4466,"style":1836},[618],[580,4468,790],{"className":4469},[955],[580,4471,1909],{"className":4472},[623],[580,4474,4476],{"className":4475},[623],[580,4477,3436],{"className":4478},[3435],[580,4480,1904],{"className":4481},[623],[580,4483],{"className":4484,"style":881},[880],[580,4486,1814],{"className":4487},[885],[580,4489],{"className":4490,"style":881},[880],[580,4492,4494,4497,4500,4503,4506],{"className":4493},[614],[580,4495],{"className":4496,"style":1836},[618],[580,4498,1821],{"className":4499},[623],[580,4501],{"className":4502,"style":881},[880],[580,4504,1814],{"className":4505},[885],[580,4507],{"className":4508,"style":881},[880],[580,4510,4512,4515,4518],{"className":4511},[614],[580,4513],{"className":4514,"style":1836},[618],[580,4516,767],{"className":4517},[623],[580,4519,808],{"className":4520},[1033],[560,4522,4524],{"id":4523},"typische-fehler","Typische Fehler",[569,4526,4527,4739,4800],{},[572,4528,4529,4530,4738],{},"Beim Mittelpunkt die Differenz statt der Summe halbieren. ",[580,4531,4533,4569],{"className":4532},[583],[580,4534,4536],{"className":4535},[587],[589,4537,4538],{"xmlns":591},[593,4539,4540,4566],{},[596,4541,4542,4548,4550,4556,4558,4564],{},[759,4543,4544,4546],{},[762,4545,764],{},[762,4547,767],{},[742,4549,790],{"stretchy":789},[736,4551,4552,4554],{"accent":610},[599,4553,803],{},[742,4555,744],{},[742,4557,1914],{},[736,4559,4560,4562],{"accent":610},[599,4561,752],{},[742,4563,744],{},[742,4565,808],{"stretchy":789},[603,4567,4568],{"encoding":605},"\\frac{1}{2}(\\vec{b} - \\vec{a})",[580,4570,4572,4694],{"className":4571,"ariaHidden":610},[609],[580,4573,4575,4579,4647,4650,4685,4688,4691],{"className":4574},[614],[580,4576],{"className":4577,"style":4578},[618],"height:1.3224em;vertical-align:-0.345em;",[580,4580,4582,4585,4644],{"className":4581},[623],[580,4583],{"className":4584},[955,956],[580,4586,4588],{"className":4587},[759],[580,4589,4591,4636],{"className":4590},[829,963],[580,4592,4594,4633],{"className":4593},[833],[580,4595,4597,4611,4619],{"className":4596,"style":970},[837],[580,4598,4599,4602],{"style":973},[580,4600],{"className":4601,"style":845},[844],[580,4603,4605],{"className":4604},[980,981,982,983],[580,4606,4608],{"className":4607},[623,983],[580,4609,767],{"className":4610},[623,983],[580,4612,4613,4616],{"style":992},[580,4614],{"className":4615,"style":845},[844],[580,4617],{"className":4618,"style":1000},[999],[580,4620,4621,4624],{"style":1003},[580,4622],{"className":4623,"style":845},[844],[580,4625,4627],{"className":4626},[980,981,982,983],[580,4628,4630],{"className":4629},[623,983],[580,4631,764],{"className":4632},[623,983],[580,4634,1020],{"className":4635},[1019],[580,4637,4639],{"className":4638},[833],[580,4640,4642],{"className":4641,"style":1027},[837],[580,4643],{},[580,4645],{"className":4646},[1033,956],[580,4648,790],{"className":4649},[955],[580,4651,4653],{"className":4652},[623,825],[580,4654,4656],{"className":4655},[829],[580,4657,4659],{"className":4658},[833],[580,4660,4662,4670],{"className":4661,"style":1233},[837],[580,4663,4664,4667],{"style":840},[580,4665],{"className":4666,"style":845},[844],[580,4668,803],{"className":4669},[623,624],[580,4671,4672,4675],{"style":1244},[580,4673],{"className":4674,"style":845},[844],[580,4676,4678],{"className":4677,"style":858},[857],[580,4679,4681],{"className":4680,"style":863},[862],[865,4682,4683],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,4684],{"d":876},[580,4686],{"className":4687,"style":934},[880],[580,4689,1914],{"className":4690},[938],[580,4692],{"className":4693,"style":934},[880],[580,4695,4697,4700,4735],{"className":4696},[614],[580,4698],{"className":4699,"style":1836},[618],[580,4701,4703],{"className":4702},[623,825],[580,4704,4706],{"className":4705},[829],[580,4707,4709],{"className":4708},[833],[580,4710,4712,4720],{"className":4711,"style":821},[837],[580,4713,4714,4717],{"style":840},[580,4715],{"className":4716,"style":845},[844],[580,4718,752],{"className":4719},[623,624],[580,4721,4722,4725],{"style":840},[580,4723],{"className":4724,"style":845},[844],[580,4726,4728],{"className":4727,"style":858},[857],[580,4729,4731],{"className":4730,"style":863},[862],[865,4732,4733],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,4734],{"d":876},[580,4736,808],{"className":4737},[1033]," ist der halbe Verbindungsvektor, kein Ortsvektor.",[572,4740,4741,4742,4770,4771,4799],{},"Beim Schwerpunkt durch ",[580,4743,4745,4758],{"className":4744},[583],[580,4746,4748],{"className":4747},[587],[589,4749,4750],{"xmlns":591},[593,4751,4752,4756],{},[596,4753,4754],{},[762,4755,767],{},[603,4757,767],{"encoding":605},[580,4759,4761],{"className":4760,"ariaHidden":610},[609],[580,4762,4764,4767],{"className":4763},[614],[580,4765],{"className":4766,"style":1371},[618],[580,4768,767],{"className":4769},[623]," statt durch ",[580,4772,4774,4787],{"className":4773},[583],[580,4775,4777],{"className":4776},[587],[589,4778,4779],{"xmlns":591},[593,4780,4781,4785],{},[596,4782,4783],{},[762,4784,1821],{},[603,4786,1821],{"encoding":605},[580,4788,4790],{"className":4789,"ariaHidden":610},[609],[580,4791,4793,4796],{"className":4792},[614],[580,4794],{"className":4795,"style":1371},[618],[580,4797,1821],{"className":4798},[623]," teilen.",[572,4801,4802,4803,4846,4847,1885,4875,4903,4904,1261],{},"Beim Parallelogramm die Reihenfolge der Ecken nicht beachten: Bei ",[580,4804,4806,4825],{"className":4805},[583],[580,4807,4809],{"className":4808},[587],[589,4810,4811],{"xmlns":591},[593,4812,4813,4823],{},[596,4814,4815,4817,4819,4821],{},[599,4816,641],{},[599,4818,644],{},[599,4820,1316],{},[599,4822,3942],{},[603,4824,3945],{"encoding":605},[580,4826,4828],{"className":4827,"ariaHidden":610},[609],[580,4829,4831,4834,4837,4840,4843],{"className":4830},[614],[580,4832],{"className":4833,"style":619},[618],[580,4835,641],{"className":4836},[623,624],[580,4838,644],{"className":4839,"style":663},[623,624],[580,4841,1316],{"className":4842,"style":1338},[623,624],[580,4844,3942],{"className":4845,"style":3967},[623,624]," liegen ",[580,4848,4850,4863],{"className":4849},[583],[580,4851,4853],{"className":4852},[587],[589,4854,4855],{"xmlns":591},[593,4856,4857,4861],{},[596,4858,4859],{},[599,4860,641],{},[603,4862,641],{"encoding":605},[580,4864,4866],{"className":4865,"ariaHidden":610},[609],[580,4867,4869,4872],{"className":4868},[614],[580,4870],{"className":4871,"style":619},[618],[580,4873,641],{"className":4874},[623,624],[580,4876,4878,4891],{"className":4877},[583],[580,4879,4881],{"className":4880},[587],[589,4882,4883],{"xmlns":591},[593,4884,4885,4889],{},[596,4886,4887],{},[599,4888,1316],{},[603,4890,1316],{"encoding":605},[580,4892,4894],{"className":4893,"ariaHidden":610},[609],[580,4895,4897,4900],{"className":4896},[614],[580,4898],{"className":4899,"style":619},[618],[580,4901,1316],{"className":4902,"style":1338},[623,624]," gegenüber, also ",[580,4905,4907,4949],{"className":4906},[583],[580,4908,4910],{"className":4909},[587],[589,4911,4912],{"xmlns":591},[593,4913,4914,4946],{},[596,4915,4916,4922,4924,4930,4932,4938,4940],{},[736,4917,4918,4920],{"accent":610},[599,4919,1456],{},[742,4921,744],{},[742,4923,747],{},[736,4925,4926,4928],{"accent":610},[599,4927,752],{},[742,4929,744],{},[742,4931,757],{},[736,4933,4934,4936],{"accent":610},[599,4935,1447],{},[742,4937,744],{},[742,4939,1914],{},[736,4941,4942,4944],{"accent":610},[599,4943,803],{},[742,4945,744],{},[603,4947,4948],{"encoding":605},"\\vec{d} = \\vec{a} + \\vec{c} - \\vec{b}",[580,4950,4952,5002,5052,5102],{"className":4951,"ariaHidden":610},[609],[580,4953,4955,4958,4993,4996,4999],{"className":4954},[614],[580,4956],{"className":4957,"style":1233},[618],[580,4959,4961],{"className":4960},[623,825],[580,4962,4964],{"className":4963},[829],[580,4965,4967],{"className":4966},[833],[580,4968,4970,4978],{"className":4969,"style":1233},[837],[580,4971,4972,4975],{"style":840},[580,4973],{"className":4974,"style":845},[844],[580,4976,1456],{"className":4977},[623,624],[580,4979,4980,4983],{"style":1244},[580,4981],{"className":4982,"style":845},[844],[580,4984,4986],{"className":4985,"style":1774},[857],[580,4987,4989],{"className":4988,"style":863},[862],[865,4990,4991],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,4992],{"d":876},[580,4994],{"className":4995,"style":881},[880],[580,4997,747],{"className":4998},[885],[580,5000],{"className":5001,"style":881},[880],[580,5003,5005,5008,5043,5046,5049],{"className":5004},[614],[580,5006],{"className":5007,"style":895},[618],[580,5009,5011],{"className":5010},[623,825],[580,5012,5014],{"className":5013},[829],[580,5015,5017],{"className":5016},[833],[580,5018,5020,5028],{"className":5019,"style":821},[837],[580,5021,5022,5025],{"style":840},[580,5023],{"className":5024,"style":845},[844],[580,5026,752],{"className":5027},[623,624],[580,5029,5030,5033],{"style":840},[580,5031],{"className":5032,"style":845},[844],[580,5034,5036],{"className":5035,"style":858},[857],[580,5037,5039],{"className":5038,"style":863},[862],[865,5040,5041],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,5042],{"d":876},[580,5044],{"className":5045,"style":934},[880],[580,5047,757],{"className":5048},[938],[580,5050],{"className":5051,"style":934},[880],[580,5053,5055,5058,5093,5096,5099],{"className":5054},[614],[580,5056],{"className":5057,"style":895},[618],[580,5059,5061],{"className":5060},[623,825],[580,5062,5064],{"className":5063},[829],[580,5065,5067],{"className":5066},[833],[580,5068,5070,5078],{"className":5069,"style":821},[837],[580,5071,5072,5075],{"style":840},[580,5073],{"className":5074,"style":845},[844],[580,5076,1447],{"className":5077},[623,624],[580,5079,5080,5083],{"style":840},[580,5081],{"className":5082,"style":845},[844],[580,5084,5086],{"className":5085,"style":1501},[857],[580,5087,5089],{"className":5088,"style":863},[862],[865,5090,5091],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,5092],{"d":876},[580,5094],{"className":5095,"style":934},[880],[580,5097,1914],{"className":5098},[938],[580,5100],{"className":5101,"style":934},[880],[580,5103,5105,5108],{"className":5104},[614],[580,5106],{"className":5107,"style":1233},[618],[580,5109,5111],{"className":5110},[623,825],[580,5112,5114],{"className":5113},[829],[580,5115,5117],{"className":5116},[833],[580,5118,5120,5128],{"className":5119,"style":1233},[837],[580,5121,5122,5125],{"style":840},[580,5123],{"className":5124,"style":845},[844],[580,5126,803],{"className":5127},[623,624],[580,5129,5130,5133],{"style":1244},[580,5131],{"className":5132,"style":845},[844],[580,5134,5136],{"className":5135,"style":858},[857],[580,5137,5139],{"className":5138,"style":863},[862],[865,5140,5141],{"xmlns":867,"width":868,"height":869,"style":870,"viewBox":871,"preserveAspectRatio":872},[874,5142],{"d":876},{"title":5144,"searchDepth":5145,"depth":5145,"links":5146},"",2,[5147,5148,5149],{"id":562,"depth":5145,"text":563},{"id":1790,"depth":5145,"text":1791},{"id":4523,"depth":5145,"text":4524},[5151,5154,5157,5159,5161,5163,5165,5167,5169,5171,5173,5176,5178,5180],{"lhs":5152,"rhs":5153},"a1 + 0.5*(b1 - a1)","(a1 + b1)\u002F2",{"lhs":5155,"rhs":5156},"a1 + 2\u002F3*((b1 + c1)\u002F2 - a1)","(a1 + b1 + c1)\u002F3",{"lhs":5158,"rhs":1821},"(1 + 5)\u002F2",{"lhs":5160,"rhs":764},"(2 + 0)\u002F2",{"lhs":5162,"rhs":764},"(3 + (-1))\u002F2",{"lhs":5164,"rhs":767},"(1 + 5 + 0)\u002F3",{"lhs":5166,"rhs":767},"(2 + 0 + 4)\u002F3",{"lhs":5168,"rhs":764},"(3 - 1 + 1)\u002F3",{"lhs":5170,"rhs":767},"1 + 2\u002F3*(2.5 - 1)",{"lhs":5172,"rhs":764},"3 + 2\u002F3*(0 - 3)",{"lhs":5174,"rhs":5175},"1 + 0 - 5","-4",{"lhs":5177,"rhs":4357},"2 + 4 - 0",{"lhs":5179,"rhs":1904},"3 + 1 - (-1)",{"lhs":5181,"rhs":5182},"(5 + (-4))\u002F2","(1 + 0)\u002F2",null,"md","centroid-vectors","\\vec{m} = \\frac{1}{2}\\left(\\vec{a} + \\vec{b}\\right), \\qquad \\vec{s} = \\frac{1}{3}\\left(\\vec{a} + \\vec{b} + \\vec{c}\\right)","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>m\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>+\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmspace width=\"2em\"\u002F>\u003Cmover accent=\"true\">\u003Cmi>s\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>+\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>+\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>c\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{m} = \\frac{1}{2}\\left(\\vec{a} + \\vec{b}\\right), \\qquad \\vec{s} = \\frac{1}{3}\\left(\\vec{a} + \\vec{b} + \\vec{c}\\right)\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.714em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">m\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size2\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9774em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size2\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1799em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size2\">(\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9774em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1799em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose delimcenter\" style=\"top:0em;\">\u003Cspan class=\"delimsizing size2\">)\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fmittelpunkt-schwerpunkt-vektoren",[],[5194,5195,5196,5197],"midpoint","vector-between-points","line-parametric-form","triangle-centroid",{"title":548,"description":5144},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fmittelpunkt-schwerpunkt-vektoren","Der Mittelpunkt einer Strecke ist das Mittel der Ortsvektoren der Endpunkte, der Schwerpunkt eines Dreiecks das der drei Ecken.",[5202,5203,5204,5205,5206],"mittelpunkt","schwerpunkt","ortsvektor","dreieck","analytische geometrie",[5208,5212,5216],{"symbol":5209,"meaning":5210,"symbolHtml":5211},"\\vec{a}, \\vec{b}, \\vec{c}","Ortsvektoren der Punkte A, B und C","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>c\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{a}, \\vec{b}, \\vec{c}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1719em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9774em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">c\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1799em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5213,"meaning":5214,"symbolHtml":5215},"\\vec{m}","Ortsvektor des Mittelpunkts M der Strecke AB","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>m\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{m}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.714em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">m\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":5217,"meaning":5218,"symbolHtml":5219},"\\vec{s}","Ortsvektor des Schwerpunkts S des Dreiecks ABC","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>s\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{s}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.714em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">s\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1799em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","8f1MtBy8hO20algHvFnnW4qgmTgMFIkHyrwEvDhVYys",[5222,5225,5228,5231],{"stem":5223,"title":5224,"category":208},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fmittelpunkt-einer-strecke","Mittelpunkt einer Strecke",{"stem":5226,"title":5227,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fschwerpunkt-dreieck","Schwerpunkt eines Dreiecks",{"stem":5229,"title":5230,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fparameterform-gerade","Parameterform einer Geraden",{"stem":5232,"title":5233,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fverbindungsvektor","Verbindungsvektor",1793824278998]