[{"data":1,"prerenderedAt":3985},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fbetrag-eines-vektors":546,"formula-related-de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fbetrag-eines-vektors":3972},[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":3916,"conditions":3935,"conditionsHtml":3935,"deprecated":3935,"description":3910,"extension":3936,"figure":3935,"figureCaption":3935,"figureHtml":3935,"formulaId":3937,"latex":3938,"latexHtml":3939,"level":3940,"meta":3941,"navigation":3942,"path":3943,"redirectFrom":3944,"related":3945,"seo":3950,"stem":3951,"subject":583,"summary":3952,"tags":3953,"variables":3959,"__hash__":3971},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fbetrag-eines-vektors.md","Betrag eines Vektors",[550,551,552,553,554,555],"Länge eines Vektors","Vektorbetrag","Betrag Vektor berechnen","Norm eines Vektors","Abstand zweier Punkte im Raum","|a|",{"type":557,"value":558,"toc":3909},"minimark",[559,564,693,1038,1257,1261,1551,2053,2386,2784,3111,3115],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,572,573,692],"p",{},"Der ",[569,570,571],"strong",{},"Betrag"," ",[574,575,578,615],"span",{"className":576},[577],"katex",[574,579,582],{"className":580},[581],"katex-mathml",[583,584,586],"math",{"xmlns":585},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[587,588,589,610],"semantics",{},[590,591,592,597,608],"mrow",{},[593,594,596],"mi",{"mathvariant":595},"normal","∣",[598,599,601,604],"mover",{"accent":600},"true",[593,602,603],{},"a",[605,606,607],"mo",{},"⃗",[593,609,596],{"mathvariant":595},[611,612,614],"annotation",{"encoding":613},"application\u002Fx-tex","|\\vec{a}|",[574,616,619],{"className":617,"ariaHidden":600},[618],"katex-html",[574,620,623,628,632,689],{"className":621},[622],"base",[574,624],{"className":625,"style":627},[626],"strut","height:1em;vertical-align:-0.25em;",[574,629,596],{"className":630},[631],"mord",[574,633,636],{"className":634},[631,635],"accent",[574,637,640],{"className":638},[639],"vlist-t",[574,641,644],{"className":642},[643],"vlist-r",[574,645,649,661],{"className":646,"style":648},[647],"vlist","height:0.714em;",[574,650,652,657],{"style":651},"top:-3em;",[574,653],{"className":654,"style":656},[655],"pstrut","height:3em;",[574,658,603],{"className":659},[631,660],"mathnormal",[574,662,663,666],{"style":651},[574,664],{"className":665,"style":656},[655],[574,667,671],{"className":668,"style":670},[669],"accent-body","left:-0.2355em;",[574,672,676],{"className":673,"style":675},[674],"overlay","height:0.714em;width:0.471em;",[677,678,685],"svg",{"xmlns":679,"width":680,"height":681,"style":682,"viewBox":683,"preserveAspectRatio":684},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.471em","0.714em","width:0.471em","0 0 471 714","xMinYMin",[686,687],"path",{"d":688},"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",[574,690,596],{"className":691},[631]," ist die Länge des Pfeils, der den Vektor darstellt. Die Formel ist der Satz des Pythagoras, zweimal angewendet: erst in der Grundfläche, dann in die Höhe.",[565,694,695,696,727,728,1037],{},"Der Betrag ist nie negativ und nur für den Nullvektor gleich ",[574,697,699,714],{"className":698},[577],[574,700,702],{"className":701},[581],[583,703,704],{"xmlns":585},[587,705,706,712],{},[590,707,708],{},[709,710,711],"mn",{},"0",[611,713,711],{"encoding":613},[574,715,717],{"className":716,"ariaHidden":600},[618],[574,718,720,724],{"className":719},[622],[574,721],{"className":722,"style":723},[626],"height:0.6444em;",[574,725,711],{"className":726},[631],". In der Ebene (2D) lautet die Formel ",[574,729,731,783],{"className":730},[577],[574,732,734],{"className":733},[581],[583,735,736],{"xmlns":585},[587,737,738,780],{},[590,739,740,742,748,750,753],{},[593,741,596],{"mathvariant":595},[598,743,744,746],{"accent":600},[593,745,603],{},[605,747,607],{},[593,749,596],{"mathvariant":595},[605,751,752],{},"=",[754,755,756],"msqrt",{},[590,757,758,769,772],{},[759,760,761,763,766],"msubsup",{},[593,762,603],{},[709,764,765],{},"1",[709,767,768],{},"2",[605,770,771],{},"+",[759,773,774,776,778],{},[593,775,603],{},[709,777,768],{},[709,779,768],{},[611,781,782],{"encoding":613},"|\\vec{a}| = \\sqrt{a_1^2 + a_2^2}",[574,784,786,845],{"className":785,"ariaHidden":600},[618],[574,787,789,792,795,830,833,838,842],{"className":788},[622],[574,790],{"className":791,"style":627},[626],[574,793,596],{"className":794},[631],[574,796,798],{"className":797},[631,635],[574,799,801],{"className":800},[639],[574,802,804],{"className":803},[643],[574,805,807,815],{"className":806,"style":648},[647],[574,808,809,812],{"style":651},[574,810],{"className":811,"style":656},[655],[574,813,603],{"className":814},[631,660],[574,816,817,820],{"style":651},[574,818],{"className":819,"style":656},[655],[574,821,823],{"className":822,"style":670},[669],[574,824,826],{"className":825,"style":675},[674],[677,827,828],{"xmlns":679,"width":680,"height":681,"style":682,"viewBox":683,"preserveAspectRatio":684},[686,829],{"d":688},[574,831,596],{"className":832},[631],[574,834],{"className":835,"style":837},[836],"mspace","margin-right:0.2778em;",[574,839,752],{"className":840},[841],"mrel",[574,843],{"className":844,"style":837},[836],[574,846,848,852],{"className":847},[622],[574,849],{"className":850,"style":851},[626],"height:1.24em;vertical-align:-0.2902em;",[574,853,856],{"className":854},[631,855],"sqrt",[574,857,860,1028],{"className":858},[639,859],"vlist-t2",[574,861,863,1025],{"className":862},[643],[574,864,867,1005],{"className":865,"style":866},[647],"height:0.9498em;",[574,868,872,876],{"className":869,"style":871},[870],"svg-align","top:-3.2em;",[574,873],{"className":874,"style":875},[655],"height:3.2em;",[574,877,880,943,947,951,954],{"className":878,"style":879},[631],"padding-left:1em;",[574,881,883,886],{"className":882},[631],[574,884,603],{"className":885},[631,660],[574,887,890],{"className":888},[889],"msupsub",[574,891,893,934],{"className":892},[639,859],[574,894,896,929],{"className":895},[643],[574,897,900,917],{"className":898,"style":899},[647],"height:0.7959em;",[574,901,903,907],{"style":902},"top:-2.4337em;margin-left:0em;margin-right:0.05em;",[574,904],{"className":905,"style":906},[655],"height:2.7em;",[574,908,914],{"className":909},[910,911,912,913],"sizing","reset-size6","size3","mtight",[574,915,765],{"className":916},[631,913],[574,918,920,923],{"style":919},"top:-3.0448em;margin-right:0.05em;",[574,921],{"className":922,"style":906},[655],[574,924,926],{"className":925},[910,911,912,913],[574,927,768],{"className":928},[631,913],[574,930,933],{"className":931},[932],"vlist-s","​",[574,935,937],{"className":936},[643],[574,938,941],{"className":939,"style":940},[647],"height:0.2663em;",[574,942],{},[574,944],{"className":945,"style":946},[836],"margin-right:0.2222em;",[574,948,771],{"className":949},[950],"mbin",[574,952],{"className":953,"style":946},[836],[574,955,957,960],{"className":956},[631],[574,958,603],{"className":959},[631,660],[574,961,963],{"className":962},[889],[574,964,966,997],{"className":965},[639,859],[574,967,969,994],{"className":968},[643],[574,970,972,983],{"className":971,"style":899},[647],[574,973,974,977],{"style":902},[574,975],{"className":976,"style":906},[655],[574,978,980],{"className":979},[910,911,912,913],[574,981,768],{"className":982},[631,913],[574,984,985,988],{"style":919},[574,986],{"className":987,"style":906},[655],[574,989,991],{"className":990},[910,911,912,913],[574,992,768],{"className":993},[631,913],[574,995,933],{"className":996},[932],[574,998,1000],{"className":999},[643],[574,1001,1003],{"className":1002,"style":940},[647],[574,1004],{},[574,1006,1008,1011],{"style":1007},"top:-2.9098em;",[574,1009],{"className":1010,"style":875},[655],[574,1012,1016],{"className":1013,"style":1015},[1014],"hide-tail","min-width:1.02em;height:1.28em;",[677,1017,1022],{"xmlns":679,"width":1018,"height":1019,"viewBox":1020,"preserveAspectRatio":1021},"400em","1.28em","0 0 400000 1296","xMinYMin slice",[686,1023],{"d":1024},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[574,1026,933],{"className":1027},[932],[574,1029,1031],{"className":1030},[643],[574,1032,1035],{"className":1033,"style":1034},[647],"height:0.2902em;",[574,1036],{},".",[565,1039,1040,1041,572,1044,1074,1075,1105,1106,1037],{},"Den ",[569,1042,1043],{},"Abstand zweier Punkte",[574,1045,1047,1061],{"className":1046},[577],[574,1048,1050],{"className":1049},[581],[583,1051,1052],{"xmlns":585},[587,1053,1054,1059],{},[590,1055,1056],{},[593,1057,1058],{},"A",[611,1060,1058],{"encoding":613},[574,1062,1064],{"className":1063,"ariaHidden":600},[618],[574,1065,1067,1071],{"className":1066},[622],[574,1068],{"className":1069,"style":1070},[626],"height:0.6833em;",[574,1072,1058],{"className":1073},[631,660]," und ",[574,1076,1078,1092],{"className":1077},[577],[574,1079,1081],{"className":1080},[581],[583,1082,1083],{"xmlns":585},[587,1084,1085,1090],{},[590,1086,1087],{},[593,1088,1089],{},"B",[611,1091,1089],{"encoding":613},[574,1093,1095],{"className":1094,"ariaHidden":600},[618],[574,1096,1098,1101],{"className":1097},[622],[574,1099],{"className":1100,"style":1070},[626],[574,1102,1089],{"className":1103,"style":1104},[631,660],"margin-right:0.0502em;"," erhält man als Betrag des Verbindungsvektors: ",[574,1107,1109,1155],{"className":1108},[577],[574,1110,1112],{"className":1111},[581],[583,1113,1114],{"xmlns":585},[587,1115,1116,1152],{},[590,1117,1118,1121,1125,1127,1130,1132,1135,1137,1139,1150],{},[593,1119,1120],{},"d",[605,1122,1124],{"stretchy":1123},"false","(",[593,1126,1058],{},[605,1128,1129],{"separator":600},",",[593,1131,1089],{},[605,1133,1134],{"stretchy":1123},")",[605,1136,752],{},[593,1138,596],{"mathvariant":595},[598,1140,1141,1147],{"accent":600},[590,1142,1143,1145],{},[593,1144,1058],{},[593,1146,1089],{},[605,1148,1149],{"stretchy":600},"→",[593,1151,596],{"mathvariant":595},[611,1153,1154],{"encoding":613},"d(A, B) = |\\overrightarrow{AB}|",[574,1156,1158,1198],{"className":1157,"ariaHidden":600},[618],[574,1159,1161,1164,1167,1171,1174,1178,1182,1185,1189,1192,1195],{"className":1160},[622],[574,1162],{"className":1163,"style":627},[626],[574,1165,1120],{"className":1166},[631,660],[574,1168,1124],{"className":1169},[1170],"mopen",[574,1172,1058],{"className":1173},[631,660],[574,1175,1129],{"className":1176},[1177],"mpunct",[574,1179],{"className":1180,"style":1181},[836],"margin-right:0.1667em;",[574,1183,1089],{"className":1184,"style":1104},[631,660],[574,1186,1134],{"className":1187},[1188],"mclose",[574,1190],{"className":1191,"style":837},[836],[574,1193,752],{"className":1194},[841],[574,1196],{"className":1197,"style":837},[836],[574,1199,1201,1205,1208,1254],{"className":1200},[622],[574,1202],{"className":1203,"style":1204},[626],"height:1.4553em;vertical-align:-0.25em;",[574,1206,596],{"className":1207},[631],[574,1209,1211],{"className":1210},[631,635],[574,1212,1214],{"className":1213},[639],[574,1215,1217],{"className":1216},[643],[574,1218,1221,1235],{"className":1219,"style":1220},[647],"height:1.2053em;",[574,1222,1223,1226],{"style":651},[574,1224],{"className":1225,"style":656},[655],[574,1227,1229,1232],{"className":1228},[631],[574,1230,1058],{"className":1231},[631,660],[574,1233,1089],{"className":1234,"style":1104},[631,660],[574,1236,1239,1242],{"className":1237,"style":1238},[870],"top:-3.6833em;",[574,1240],{"className":1241,"style":656},[655],[574,1243,1246],{"className":1244,"style":1245},[1014],"height:0.522em;min-width:0.888em;",[677,1247,1251],{"xmlns":679,"width":1018,"height":1248,"viewBox":1249,"preserveAspectRatio":1250},"0.522em","0 0 400000 522","xMaxYMin slice",[686,1252],{"d":1253},"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",[574,1255,596],{"className":1256},[631],[560,1258,1260],{"id":1259},"beispiele","Beispiele",[565,1262,1263,1264,1550],{},"Für ",[574,1265,1267,1331],{"className":1266},[577],[574,1268,1270],{"className":1269},[581],[583,1271,1272],{"xmlns":585},[587,1273,1274,1328],{},[590,1275,1276,1282,1284],{},[598,1277,1278,1280],{"accent":600},[593,1279,603],{},[605,1281,607],{},[605,1283,752],{},[590,1285,1286,1288,1326],{},[605,1287,1124],{"fence":600},[1289,1290,1294,1305,1318],"mtable",{"rowspacing":1291,"columnalign":1292,"columnspacing":1293},"0.16em","center","1em",[1295,1296,1297],"mtr",{},[1298,1299,1300],"mtd",{},[1301,1302,1303],"mstyle",{"scriptlevel":711,"displaystyle":1123},[709,1304,768],{},[1295,1306,1307],{},[1298,1308,1309],{},[1301,1310,1311],{"scriptlevel":711,"displaystyle":1123},[590,1312,1313,1316],{},[605,1314,1315],{},"−",[709,1317,765],{},[1295,1319,1320],{},[1298,1321,1322],{},[1301,1323,1324],{"scriptlevel":711,"displaystyle":1123},[709,1325,768],{},[605,1327,1134],{"fence":600},[611,1329,1330],{"encoding":613},"\\vec{a} = \\begin{pmatrix} 2 \\\\ -1 \\\\ 2 \\end{pmatrix}",[574,1332,1334,1384],{"className":1333,"ariaHidden":600},[618],[574,1335,1337,1340,1375,1378,1381],{"className":1336},[622],[574,1338],{"className":1339,"style":648},[626],[574,1341,1343],{"className":1342},[631,635],[574,1344,1346],{"className":1345},[639],[574,1347,1349],{"className":1348},[643],[574,1350,1352,1360],{"className":1351,"style":648},[647],[574,1353,1354,1357],{"style":651},[574,1355],{"className":1356,"style":656},[655],[574,1358,603],{"className":1359},[631,660],[574,1361,1362,1365],{"style":651},[574,1363],{"className":1364,"style":656},[655],[574,1366,1368],{"className":1367,"style":670},[669],[574,1369,1371],{"className":1370,"style":675},[674],[677,1372,1373],{"xmlns":679,"width":680,"height":681,"style":682,"viewBox":683,"preserveAspectRatio":684},[686,1374],{"d":688},[574,1376],{"className":1377,"style":837},[836],[574,1379,752],{"className":1380},[841],[574,1382],{"className":1383,"style":837},[836],[574,1385,1387,1391],{"className":1386},[622],[574,1388],{"className":1389,"style":1390},[626],"height:3.6em;vertical-align:-1.55em;",[574,1392,1395,1443,1512],{"className":1393},[1394],"minner",[574,1396,1398],{"className":1397},[1170],[574,1399,1403],{"className":1400},[1401,1402],"delimsizing","mult",[574,1404,1406,1434],{"className":1405},[639,859],[574,1407,1409,1431],{"className":1408},[643],[574,1410,1413],{"className":1411,"style":1412},[647],"height:2.05em;",[574,1414,1416,1420],{"style":1415},"top:-4.05em;",[574,1417],{"className":1418,"style":1419},[655],"height:5.6em;",[574,1421,1423],{"style":1422},"width:0.875em;height:3.6em;",[677,1424,1428],{"xmlns":679,"width":1425,"height":1426,"viewBox":1427},"0.875em","3.6em","0 0 875 3600",[686,1429],{"d":1430},"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",[574,1432,933],{"className":1433},[932],[574,1435,1437],{"className":1436},[643],[574,1438,1441],{"className":1439,"style":1440},[647],"height:1.55em;",[574,1442],{},[574,1444,1446],{"className":1445},[631],[574,1447,1449],{"className":1448},[1289],[574,1450,1453],{"className":1451},[1452],"col-align-c",[574,1454,1456,1504],{"className":1455},[639,859],[574,1457,1459,1501],{"className":1458},[643],[574,1460,1462,1474,1489],{"className":1461,"style":1412},[647],[574,1463,1465,1468],{"style":1464},"top:-4.21em;",[574,1466],{"className":1467,"style":656},[655],[574,1469,1471],{"className":1470},[631],[574,1472,768],{"className":1473},[631],[574,1475,1477,1480],{"style":1476},"top:-3.01em;",[574,1478],{"className":1479,"style":656},[655],[574,1481,1483,1486],{"className":1482},[631],[574,1484,1315],{"className":1485},[631],[574,1487,765],{"className":1488},[631],[574,1490,1492,1495],{"style":1491},"top:-1.81em;",[574,1493],{"className":1494,"style":656},[655],[574,1496,1498],{"className":1497},[631],[574,1499,768],{"className":1500},[631],[574,1502,933],{"className":1503},[932],[574,1505,1507],{"className":1506},[643],[574,1508,1510],{"className":1509,"style":1440},[647],[574,1511],{},[574,1513,1515],{"className":1514},[1188],[574,1516,1518],{"className":1517},[1401,1402],[574,1519,1521,1542],{"className":1520},[639,859],[574,1522,1524,1539],{"className":1523},[643],[574,1525,1527],{"className":1526,"style":1412},[647],[574,1528,1529,1532],{"style":1415},[574,1530],{"className":1531,"style":1419},[655],[574,1533,1534],{"style":1422},[677,1535,1536],{"xmlns":679,"width":1425,"height":1426,"viewBox":1427},[686,1537],{"d":1538},"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",[574,1540,933],{"className":1541},[932],[574,1543,1545],{"className":1544},[643],[574,1546,1548],{"className":1547,"style":1440},[647],[574,1549],{},":",[574,1552,1555],{"className":1553},[1554],"katex-display",[574,1556,1558,1645],{"className":1557},[577],[574,1559,1561],{"className":1560},[581],[583,1562,1564],{"xmlns":585,"display":1563},"block",[587,1565,1566,1642],{},[590,1567,1568,1570,1576,1578,1580,1613,1615,1630,1632,1637,1639],{},[593,1569,596],{"mathvariant":595},[598,1571,1572,1574],{"accent":600},[593,1573,603],{},[605,1575,607],{},[593,1577,596],{"mathvariant":595},[605,1579,752],{},[754,1581,1582],{},[590,1583,1584,1591,1593,1595,1597,1599,1605,1607],{},[1585,1586,1587,1589],"msup",{},[709,1588,768],{},[709,1590,768],{},[605,1592,771],{},[605,1594,1124],{"stretchy":1123},[605,1596,1315],{},[709,1598,765],{},[1585,1600,1601,1603],{},[605,1602,1134],{"stretchy":1123},[709,1604,768],{},[605,1606,771],{},[1585,1608,1609,1611],{},[709,1610,768],{},[709,1612,768],{},[605,1614,752],{},[754,1616,1617],{},[590,1618,1619,1622,1624,1626,1628],{},[709,1620,1621],{},"4",[605,1623,771],{},[709,1625,765],{},[605,1627,771],{},[709,1629,1621],{},[605,1631,752],{},[754,1633,1634],{},[709,1635,1636],{},"9",[605,1638,752],{},[709,1640,1641],{},"3",[611,1643,1644],{"encoding":613},"|\\vec{a}| = \\sqrt{2^2 + (-1)^2 + 2^2} = \\sqrt{4 + 1 + 4} = \\sqrt{9} = 3",[574,1646,1648,1704,1883,1978,2044],{"className":1647,"ariaHidden":600},[618],[574,1649,1651,1654,1657,1692,1695,1698,1701],{"className":1650},[622],[574,1652],{"className":1653,"style":627},[626],[574,1655,596],{"className":1656},[631],[574,1658,1660],{"className":1659},[631,635],[574,1661,1663],{"className":1662},[639],[574,1664,1666],{"className":1665},[643],[574,1667,1669,1677],{"className":1668,"style":648},[647],[574,1670,1671,1674],{"style":651},[574,1672],{"className":1673,"style":656},[655],[574,1675,603],{"className":1676},[631,660],[574,1678,1679,1682],{"style":651},[574,1680],{"className":1681,"style":656},[655],[574,1683,1685],{"className":1684,"style":670},[669],[574,1686,1688],{"className":1687,"style":675},[674],[677,1689,1690],{"xmlns":679,"width":680,"height":681,"style":682,"viewBox":683,"preserveAspectRatio":684},[686,1691],{"d":688},[574,1693,596],{"className":1694},[631],[574,1696],{"className":1697,"style":837},[836],[574,1699,752],{"className":1700},[841],[574,1702],{"className":1703,"style":837},[836],[574,1705,1707,1711,1874,1877,1880],{"className":1706},[622],[574,1708],{"className":1709,"style":1710},[626],"height:1.24em;vertical-align:-0.2561em;",[574,1712,1714],{"className":1713},[631,855],[574,1715,1717,1865],{"className":1716},[639,859],[574,1718,1720,1862],{"className":1719},[643],[574,1721,1724,1849],{"className":1722,"style":1723},[647],"height:0.9839em;",[574,1725,1727,1730],{"className":1726,"style":871},[870],[574,1728],{"className":1729,"style":875},[655],[574,1731,1733,1764,1767,1770,1773,1776,1779,1782,1811,1814,1817,1820],{"className":1732,"style":879},[631],[574,1734,1736,1739],{"className":1735},[631],[574,1737,768],{"className":1738},[631],[574,1740,1742],{"className":1741},[889],[574,1743,1745],{"className":1744},[639],[574,1746,1748],{"className":1747},[643],[574,1749,1752],{"className":1750,"style":1751},[647],"height:0.7401em;",[574,1753,1755,1758],{"style":1754},"top:-2.989em;margin-right:0.05em;",[574,1756],{"className":1757,"style":906},[655],[574,1759,1761],{"className":1760},[910,911,912,913],[574,1762,768],{"className":1763},[631,913],[574,1765],{"className":1766,"style":946},[836],[574,1768,771],{"className":1769},[950],[574,1771],{"className":1772,"style":946},[836],[574,1774,1124],{"className":1775},[1170],[574,1777,1315],{"className":1778},[631],[574,1780,765],{"className":1781},[631],[574,1783,1785,1788],{"className":1784},[1188],[574,1786,1134],{"className":1787},[1188],[574,1789,1791],{"className":1790},[889],[574,1792,1794],{"className":1793},[639],[574,1795,1797],{"className":1796},[643],[574,1798,1800],{"className":1799,"style":1751},[647],[574,1801,1802,1805],{"style":1754},[574,1803],{"className":1804,"style":906},[655],[574,1806,1808],{"className":1807},[910,911,912,913],[574,1809,768],{"className":1810},[631,913],[574,1812],{"className":1813,"style":946},[836],[574,1815,771],{"className":1816},[950],[574,1818],{"className":1819,"style":946},[836],[574,1821,1823,1826],{"className":1822},[631],[574,1824,768],{"className":1825},[631],[574,1827,1829],{"className":1828},[889],[574,1830,1832],{"className":1831},[639],[574,1833,1835],{"className":1834},[643],[574,1836,1838],{"className":1837,"style":1751},[647],[574,1839,1840,1843],{"style":1754},[574,1841],{"className":1842,"style":906},[655],[574,1844,1846],{"className":1845},[910,911,912,913],[574,1847,768],{"className":1848},[631,913],[574,1850,1852,1855],{"style":1851},"top:-2.9439em;",[574,1853],{"className":1854,"style":875},[655],[574,1856,1858],{"className":1857,"style":1015},[1014],[677,1859,1860],{"xmlns":679,"width":1018,"height":1019,"viewBox":1020,"preserveAspectRatio":1021},[686,1861],{"d":1024},[574,1863,933],{"className":1864},[932],[574,1866,1868],{"className":1867},[643],[574,1869,1872],{"className":1870,"style":1871},[647],"height:0.2561em;",[574,1873],{},[574,1875],{"className":1876,"style":837},[836],[574,1878,752],{"className":1879},[841],[574,1881],{"className":1882,"style":837},[836],[574,1884,1886,1890,1969,1972,1975],{"className":1885},[622],[574,1887],{"className":1888,"style":1889},[626],"height:1.04em;vertical-align:-0.1256em;",[574,1891,1893],{"className":1892},[631,855],[574,1894,1896,1960],{"className":1895},[639,859],[574,1897,1899,1957],{"className":1898},[643],[574,1900,1903,1940],{"className":1901,"style":1902},[647],"height:0.9144em;",[574,1904,1906,1909],{"className":1905,"style":651},[870],[574,1907],{"className":1908,"style":656},[655],[574,1910,1913,1916,1919,1922,1925,1928,1931,1934,1937],{"className":1911,"style":1912},[631],"padding-left:0.833em;",[574,1914,1621],{"className":1915},[631],[574,1917],{"className":1918,"style":946},[836],[574,1920,771],{"className":1921},[950],[574,1923],{"className":1924,"style":946},[836],[574,1926,765],{"className":1927},[631],[574,1929],{"className":1930,"style":946},[836],[574,1932,771],{"className":1933},[950],[574,1935],{"className":1936,"style":946},[836],[574,1938,1621],{"className":1939},[631],[574,1941,1943,1946],{"style":1942},"top:-2.8744em;",[574,1944],{"className":1945,"style":656},[655],[574,1947,1950],{"className":1948,"style":1949},[1014],"min-width:0.853em;height:1.08em;",[677,1951,1954],{"xmlns":679,"width":1018,"height":1952,"viewBox":1953,"preserveAspectRatio":1021},"1.08em","0 0 400000 1080",[686,1955],{"d":1956},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[574,1958,933],{"className":1959},[932],[574,1961,1963],{"className":1962},[643],[574,1964,1967],{"className":1965,"style":1966},[647],"height:0.1256em;",[574,1968],{},[574,1970],{"className":1971,"style":837},[836],[574,1973,752],{"className":1974},[841],[574,1976],{"className":1977,"style":837},[836],[574,1979,1981,1985,2035,2038,2041],{"className":1980},[622],[574,1982],{"className":1983,"style":1984},[626],"height:1.04em;vertical-align:-0.0839em;",[574,1986,1988],{"className":1987},[631,855],[574,1989,1991,2026],{"className":1990},[639,859],[574,1992,1994,2023],{"className":1993},[643],[574,1995,1998,2010],{"className":1996,"style":1997},[647],"height:0.9561em;",[574,1999,2001,2004],{"className":2000,"style":651},[870],[574,2002],{"className":2003,"style":656},[655],[574,2005,2007],{"className":2006,"style":1912},[631],[574,2008,1636],{"className":2009},[631],[574,2011,2013,2016],{"style":2012},"top:-2.9161em;",[574,2014],{"className":2015,"style":656},[655],[574,2017,2019],{"className":2018,"style":1949},[1014],[677,2020,2021],{"xmlns":679,"width":1018,"height":1952,"viewBox":1953,"preserveAspectRatio":1021},[686,2022],{"d":1956},[574,2024,933],{"className":2025},[932],[574,2027,2029],{"className":2028},[643],[574,2030,2033],{"className":2031,"style":2032},[647],"height:0.0839em;",[574,2034],{},[574,2036],{"className":2037,"style":837},[836],[574,2039,752],{"className":2040},[841],[574,2042],{"className":2043,"style":837},[836],[574,2045,2047,2050],{"className":2046},[622],[574,2048],{"className":2049,"style":723},[626],[574,2051,1641],{"className":2052},[631],[565,2054,2055,2056,1074,2149,2237,2238,1550],{},"Abstand von ",[574,2057,2059,2089],{"className":2058},[577],[574,2060,2062],{"className":2061},[581],[583,2063,2064],{"xmlns":585},[587,2065,2066,2086],{},[590,2067,2068,2070,2072,2074,2076,2078,2080,2082,2084],{},[593,2069,1058],{},[605,2071,1124],{"stretchy":1123},[709,2073,765],{},[605,2075,596],{},[709,2077,768],{},[605,2079,596],{},[605,2081,1315],{},[709,2083,765],{},[605,2085,1134],{"stretchy":1123},[611,2087,2088],{"encoding":613},"A(1 \\mid 2 \\mid -1)",[574,2090,2092,2116,2134],{"className":2091,"ariaHidden":600},[618],[574,2093,2095,2098,2101,2104,2107,2110,2113],{"className":2094},[622],[574,2096],{"className":2097,"style":627},[626],[574,2099,1058],{"className":2100},[631,660],[574,2102,1124],{"className":2103},[1170],[574,2105,765],{"className":2106},[631],[574,2108],{"className":2109,"style":837},[836],[574,2111,596],{"className":2112},[841],[574,2114],{"className":2115,"style":837},[836],[574,2117,2119,2122,2125,2128,2131],{"className":2118},[622],[574,2120],{"className":2121,"style":627},[626],[574,2123,768],{"className":2124},[631],[574,2126],{"className":2127,"style":837},[836],[574,2129,596],{"className":2130},[841],[574,2132],{"className":2133,"style":837},[836],[574,2135,2137,2140,2143,2146],{"className":2136},[622],[574,2138],{"className":2139,"style":627},[626],[574,2141,1315],{"className":2142},[631],[574,2144,765],{"className":2145},[631],[574,2147,1134],{"className":2148},[1188],[574,2150,2152,2180],{"className":2151},[577],[574,2153,2155],{"className":2154},[581],[583,2156,2157],{"xmlns":585},[587,2158,2159,2177],{},[590,2160,2161,2163,2165,2167,2169,2171,2173,2175],{},[593,2162,1089],{},[605,2164,1124],{"stretchy":1123},[709,2166,1621],{},[605,2168,596],{},[709,2170,711],{},[605,2172,596],{},[709,2174,1641],{},[605,2176,1134],{"stretchy":1123},[611,2178,2179],{"encoding":613},"B(4 \\mid 0 \\mid 3)",[574,2181,2183,2207,2225],{"className":2182,"ariaHidden":600},[618],[574,2184,2186,2189,2192,2195,2198,2201,2204],{"className":2185},[622],[574,2187],{"className":2188,"style":627},[626],[574,2190,1089],{"className":2191,"style":1104},[631,660],[574,2193,1124],{"className":2194},[1170],[574,2196,1621],{"className":2197},[631],[574,2199],{"className":2200,"style":837},[836],[574,2202,596],{"className":2203},[841],[574,2205],{"className":2206,"style":837},[836],[574,2208,2210,2213,2216,2219,2222],{"className":2209},[622],[574,2211],{"className":2212,"style":627},[626],[574,2214,711],{"className":2215},[631],[574,2217],{"className":2218,"style":837},[836],[574,2220,596],{"className":2221},[841],[574,2223],{"className":2224,"style":837},[836],[574,2226,2228,2231,2234],{"className":2227},[622],[574,2229],{"className":2230,"style":627},[626],[574,2232,1641],{"className":2233},[631],[574,2235,1134],{"className":2236},[1188],". Der Verbindungsvektor ist ",[574,2239,2241,2287],{"className":2240},[577],[574,2242,2244],{"className":2243},[581],[583,2245,2246],{"xmlns":585},[587,2247,2248,2284],{},[590,2249,2250,2260,2262,2264,2266,2268,2272,2274,2276,2278,2280,2282],{},[598,2251,2252,2258],{"accent":600},[590,2253,2254,2256],{},[593,2255,1058],{},[593,2257,1089],{},[605,2259,1149],{"stretchy":600},[605,2261,752],{},[605,2263,1124],{"stretchy":1123},[709,2265,1641],{},[605,2267,1129],{"separator":600},[2269,2270,2271],"mtext",{}," ",[605,2273,1315],{},[709,2275,768],{},[605,2277,1129],{"separator":600},[2269,2279,2271],{},[709,2281,1621],{},[605,2283,1134],{"stretchy":1123},[611,2285,2286],{"encoding":613},"\\overrightarrow{AB} = (3,\\ -2,\\ 4)",[574,2288,2290,2344],{"className":2289,"ariaHidden":600},[618],[574,2291,2293,2296,2335,2338,2341],{"className":2292},[622],[574,2294],{"className":2295,"style":1220},[626],[574,2297,2299],{"className":2298},[631,635],[574,2300,2302],{"className":2301},[639],[574,2303,2305],{"className":2304},[643],[574,2306,2308,2322],{"className":2307,"style":1220},[647],[574,2309,2310,2313],{"style":651},[574,2311],{"className":2312,"style":656},[655],[574,2314,2316,2319],{"className":2315},[631],[574,2317,1058],{"className":2318},[631,660],[574,2320,1089],{"className":2321,"style":1104},[631,660],[574,2323,2325,2328],{"className":2324,"style":1238},[870],[574,2326],{"className":2327,"style":656},[655],[574,2329,2331],{"className":2330,"style":1245},[1014],[677,2332,2333],{"xmlns":679,"width":1018,"height":1248,"viewBox":1249,"preserveAspectRatio":1250},[686,2334],{"d":1253},[574,2336],{"className":2337,"style":837},[836],[574,2339,752],{"className":2340},[841],[574,2342],{"className":2343,"style":837},[836],[574,2345,2347,2350,2353,2356,2359,2362,2365,2368,2371,2374,2377,2380,2383],{"className":2346},[622],[574,2348],{"className":2349,"style":627},[626],[574,2351,1124],{"className":2352},[1170],[574,2354,1641],{"className":2355},[631],[574,2357,1129],{"className":2358},[1177],[574,2360,2271],{"className":2361},[836],[574,2363],{"className":2364,"style":1181},[836],[574,2366,1315],{"className":2367},[631],[574,2369,768],{"className":2370},[631],[574,2372,1129],{"className":2373},[1177],[574,2375,2271],{"className":2376},[836],[574,2378],{"className":2379,"style":1181},[836],[574,2381,1621],{"className":2382},[631],[574,2384,1134],{"className":2385},[1188],[574,2387,2389],{"className":2388},[1554],[574,2390,2392,2465],{"className":2391},[577],[574,2393,2395],{"className":2394},[581],[583,2396,2397],{"xmlns":585,"display":1563},[587,2398,2399,2462],{},[590,2400,2401,2403,2413,2415,2417,2449,2451,2456,2459],{},[593,2402,596],{"mathvariant":595},[598,2404,2405,2411],{"accent":600},[590,2406,2407,2409],{},[593,2408,1058],{},[593,2410,1089],{},[605,2412,1149],{"stretchy":600},[593,2414,596],{"mathvariant":595},[605,2416,752],{},[754,2418,2419],{},[590,2420,2421,2427,2429,2431,2433,2435,2441,2443],{},[1585,2422,2423,2425],{},[709,2424,1641],{},[709,2426,768],{},[605,2428,771],{},[605,2430,1124],{"stretchy":1123},[605,2432,1315],{},[709,2434,768],{},[1585,2436,2437,2439],{},[605,2438,1134],{"stretchy":1123},[709,2440,768],{},[605,2442,771],{},[1585,2444,2445,2447],{},[709,2446,1621],{},[709,2448,768],{},[605,2450,752],{},[754,2452,2453],{},[709,2454,2455],{},"29",[605,2457,2458],{},"≈",[709,2460,2461],{},"5,39",[611,2463,2464],{"encoding":613},"|\\overrightarrow{AB}| = \\sqrt{3^2 + (-2)^2 + 4^2} = \\sqrt{29} \\approx 5{,}39",[574,2466,2468,2528,2701,2763],{"className":2467,"ariaHidden":600},[618],[574,2469,2471,2474,2477,2516,2519,2522,2525],{"className":2470},[622],[574,2472],{"className":2473,"style":1204},[626],[574,2475,596],{"className":2476},[631],[574,2478,2480],{"className":2479},[631,635],[574,2481,2483],{"className":2482},[639],[574,2484,2486],{"className":2485},[643],[574,2487,2489,2503],{"className":2488,"style":1220},[647],[574,2490,2491,2494],{"style":651},[574,2492],{"className":2493,"style":656},[655],[574,2495,2497,2500],{"className":2496},[631],[574,2498,1058],{"className":2499},[631,660],[574,2501,1089],{"className":2502,"style":1104},[631,660],[574,2504,2506,2509],{"className":2505,"style":1238},[870],[574,2507],{"className":2508,"style":656},[655],[574,2510,2512],{"className":2511,"style":1245},[1014],[677,2513,2514],{"xmlns":679,"width":1018,"height":1248,"viewBox":1249,"preserveAspectRatio":1250},[686,2515],{"d":1253},[574,2517,596],{"className":2518},[631],[574,2520],{"className":2521,"style":837},[836],[574,2523,752],{"className":2524},[841],[574,2526],{"className":2527,"style":837},[836],[574,2529,2531,2534,2692,2695,2698],{"className":2530},[622],[574,2532],{"className":2533,"style":1710},[626],[574,2535,2537],{"className":2536},[631,855],[574,2538,2540,2684],{"className":2539},[639,859],[574,2541,2543,2681],{"className":2542},[643],[574,2544,2546,2669],{"className":2545,"style":1723},[647],[574,2547,2549,2552],{"className":2548,"style":871},[870],[574,2550],{"className":2551,"style":875},[655],[574,2553,2555,2584,2587,2590,2593,2596,2599,2602,2631,2634,2637,2640],{"className":2554,"style":879},[631],[574,2556,2558,2561],{"className":2557},[631],[574,2559,1641],{"className":2560},[631],[574,2562,2564],{"className":2563},[889],[574,2565,2567],{"className":2566},[639],[574,2568,2570],{"className":2569},[643],[574,2571,2573],{"className":2572,"style":1751},[647],[574,2574,2575,2578],{"style":1754},[574,2576],{"className":2577,"style":906},[655],[574,2579,2581],{"className":2580},[910,911,912,913],[574,2582,768],{"className":2583},[631,913],[574,2585],{"className":2586,"style":946},[836],[574,2588,771],{"className":2589},[950],[574,2591],{"className":2592,"style":946},[836],[574,2594,1124],{"className":2595},[1170],[574,2597,1315],{"className":2598},[631],[574,2600,768],{"className":2601},[631],[574,2603,2605,2608],{"className":2604},[1188],[574,2606,1134],{"className":2607},[1188],[574,2609,2611],{"className":2610},[889],[574,2612,2614],{"className":2613},[639],[574,2615,2617],{"className":2616},[643],[574,2618,2620],{"className":2619,"style":1751},[647],[574,2621,2622,2625],{"style":1754},[574,2623],{"className":2624,"style":906},[655],[574,2626,2628],{"className":2627},[910,911,912,913],[574,2629,768],{"className":2630},[631,913],[574,2632],{"className":2633,"style":946},[836],[574,2635,771],{"className":2636},[950],[574,2638],{"className":2639,"style":946},[836],[574,2641,2643,2646],{"className":2642},[631],[574,2644,1621],{"className":2645},[631],[574,2647,2649],{"className":2648},[889],[574,2650,2652],{"className":2651},[639],[574,2653,2655],{"className":2654},[643],[574,2656,2658],{"className":2657,"style":1751},[647],[574,2659,2660,2663],{"style":1754},[574,2661],{"className":2662,"style":906},[655],[574,2664,2666],{"className":2665},[910,911,912,913],[574,2667,768],{"className":2668},[631,913],[574,2670,2671,2674],{"style":1851},[574,2672],{"className":2673,"style":875},[655],[574,2675,2677],{"className":2676,"style":1015},[1014],[677,2678,2679],{"xmlns":679,"width":1018,"height":1019,"viewBox":1020,"preserveAspectRatio":1021},[686,2680],{"d":1024},[574,2682,933],{"className":2683},[932],[574,2685,2687],{"className":2686},[643],[574,2688,2690],{"className":2689,"style":1871},[647],[574,2691],{},[574,2693],{"className":2694,"style":837},[836],[574,2696,752],{"className":2697},[841],[574,2699],{"className":2700,"style":837},[836],[574,2702,2704,2707,2754,2757,2760],{"className":2703},[622],[574,2705],{"className":2706,"style":1984},[626],[574,2708,2710],{"className":2709},[631,855],[574,2711,2713,2746],{"className":2712},[639,859],[574,2714,2716,2743],{"className":2715},[643],[574,2717,2719,2731],{"className":2718,"style":1997},[647],[574,2720,2722,2725],{"className":2721,"style":651},[870],[574,2723],{"className":2724,"style":656},[655],[574,2726,2728],{"className":2727,"style":1912},[631],[574,2729,2455],{"className":2730},[631],[574,2732,2733,2736],{"style":2012},[574,2734],{"className":2735,"style":656},[655],[574,2737,2739],{"className":2738,"style":1949},[1014],[677,2740,2741],{"xmlns":679,"width":1018,"height":1952,"viewBox":1953,"preserveAspectRatio":1021},[686,2742],{"d":1956},[574,2744,933],{"className":2745},[932],[574,2747,2749],{"className":2748},[643],[574,2750,2752],{"className":2751,"style":2032},[647],[574,2753],{},[574,2755],{"className":2756,"style":837},[836],[574,2758,2458],{"className":2759},[841],[574,2761],{"className":2762,"style":837},[836],[574,2764,2766,2770,2774,2780],{"className":2765},[622],[574,2767],{"className":2768,"style":2769},[626],"height:0.8389em;vertical-align:-0.1944em;",[574,2771,2773],{"className":2772},[631],"5",[574,2775,2777],{"className":2776},[631],[574,2778,1129],{"className":2779},[1177],[574,2781,2783],{"className":2782},[631],"39",[565,2785,2786,2787,1037],{},"In der Ebene: ",[574,2788,2790,2849],{"className":2789},[577],[574,2791,2793],{"className":2792},[581],[583,2794,2795],{"xmlns":585},[587,2796,2797,2846],{},[590,2798,2799,2829,2831,2842,2844],{},[590,2800,2801,2803,2827],{},[605,2802,596],{"fence":600},[590,2804,2805,2807,2825],{},[605,2806,1124],{"fence":600},[1289,2808,2809,2817],{"rowspacing":1291,"columnalign":1292,"columnspacing":1293},[1295,2810,2811],{},[1298,2812,2813],{},[1301,2814,2815],{"scriptlevel":711,"displaystyle":1123},[709,2816,1641],{},[1295,2818,2819],{},[1298,2820,2821],{},[1301,2822,2823],{"scriptlevel":711,"displaystyle":1123},[709,2824,1621],{},[605,2826,1134],{"fence":600},[605,2828,596],{"fence":600},[605,2830,752],{},[754,2832,2833],{},[590,2834,2835,2837,2839],{},[709,2836,1636],{},[605,2838,771],{},[709,2840,2841],{},"16",[605,2843,752],{},[709,2845,2773],{},[611,2847,2848],{"encoding":613},"\\left|\\begin{pmatrix} 3 \\\\ 4 \\end{pmatrix}\\right| = \\sqrt{9 + 16} = 5",[574,2850,2852,3024,3102],{"className":2851,"ariaHidden":600},[618],[574,2853,2855,2859,3015,3018,3021],{"className":2854},[622],[574,2856],{"className":2857,"style":2858},[626],"height:2.4em;vertical-align:-0.95em;",[574,2860,2862,2908,2978],{"className":2861},[1394],[574,2863,2865],{"className":2864},[1170],[574,2866,2868],{"className":2867},[1401,1402],[574,2869,2871,2899],{"className":2870},[639,859],[574,2872,2874,2896],{"className":2873},[643],[574,2875,2878],{"className":2876,"style":2877},[647],"height:1.45em;",[574,2879,2881,2885],{"style":2880},"top:-3.45em;",[574,2882],{"className":2883,"style":2884},[655],"height:4.4em;",[574,2886,2888],{"style":2887},"width:0.333em;height:2.4em;",[677,2889,2893],{"xmlns":679,"width":2890,"height":2891,"viewBox":2892},"0.333em","2.4em","0 0 333 2400",[686,2894],{"d":2895},"M145 15 v585 v1200 v585 c2.667,10,9.667,15,21,15\nc10,0,16.667,-5,20,-15 v-585 v-1200 v-585 c-2.667,-10,-9.667,-15,-21,-15\nc-10,0,-16.667,5,-20,15z M188 15 H145 v585 v1200 v585 h43z",[574,2897,933],{"className":2898},[932],[574,2900,2902],{"className":2901},[643],[574,2903,2906],{"className":2904,"style":2905},[647],"height:0.95em;",[574,2907],{},[574,2909,2911,2919,2972],{"className":2910},[1394],[574,2912,2916],{"className":2913,"style":2915},[1170,2914],"delimcenter","top:0em;",[574,2917,1124],{"className":2918},[1401,912],[574,2920,2922],{"className":2921},[631],[574,2923,2925],{"className":2924},[1289],[574,2926,2928],{"className":2927},[1452],[574,2929,2931,2964],{"className":2930},[639,859],[574,2932,2934,2961],{"className":2933},[643],[574,2935,2937,2949],{"className":2936,"style":2877},[647],[574,2938,2940,2943],{"style":2939},"top:-3.61em;",[574,2941],{"className":2942,"style":656},[655],[574,2944,2946],{"className":2945},[631],[574,2947,1641],{"className":2948},[631],[574,2950,2952,2955],{"style":2951},"top:-2.41em;",[574,2953],{"className":2954,"style":656},[655],[574,2956,2958],{"className":2957},[631],[574,2959,1621],{"className":2960},[631],[574,2962,933],{"className":2963},[932],[574,2965,2967],{"className":2966},[643],[574,2968,2970],{"className":2969,"style":2905},[647],[574,2971],{},[574,2973,2975],{"className":2974,"style":2915},[1188,2914],[574,2976,1134],{"className":2977},[1401,912],[574,2979,2981],{"className":2980},[1188],[574,2982,2984],{"className":2983},[1401,1402],[574,2985,2987,3007],{"className":2986},[639,859],[574,2988,2990,3004],{"className":2989},[643],[574,2991,2993],{"className":2992,"style":2877},[647],[574,2994,2995,2998],{"style":2880},[574,2996],{"className":2997,"style":2884},[655],[574,2999,3000],{"style":2887},[677,3001,3002],{"xmlns":679,"width":2890,"height":2891,"viewBox":2892},[686,3003],{"d":2895},[574,3005,933],{"className":3006},[932],[574,3008,3010],{"className":3009},[643],[574,3011,3013],{"className":3012,"style":2905},[647],[574,3014],{},[574,3016],{"className":3017,"style":837},[836],[574,3019,752],{"className":3020},[841],[574,3022],{"className":3023,"style":837},[836],[574,3025,3027,3031,3093,3096,3099],{"className":3026},[622],[574,3028],{"className":3029,"style":3030},[626],"height:1.04em;vertical-align:-0.1744em;",[574,3032,3034],{"className":3033},[631,855],[574,3035,3037,3084],{"className":3036},[639,859],[574,3038,3040,3081],{"className":3039},[643],[574,3041,3044,3068],{"className":3042,"style":3043},[647],"height:0.8656em;",[574,3045,3047,3050],{"className":3046,"style":651},[870],[574,3048],{"className":3049,"style":656},[655],[574,3051,3053,3056,3059,3062,3065],{"className":3052,"style":1912},[631],[574,3054,1636],{"className":3055},[631],[574,3057],{"className":3058,"style":946},[836],[574,3060,771],{"className":3061},[950],[574,3063],{"className":3064,"style":946},[836],[574,3066,2841],{"className":3067},[631],[574,3069,3071,3074],{"style":3070},"top:-2.8256em;",[574,3072],{"className":3073,"style":656},[655],[574,3075,3077],{"className":3076,"style":1949},[1014],[677,3078,3079],{"xmlns":679,"width":1018,"height":1952,"viewBox":1953,"preserveAspectRatio":1021},[686,3080],{"d":1956},[574,3082,933],{"className":3083},[932],[574,3085,3087],{"className":3086},[643],[574,3088,3091],{"className":3089,"style":3090},[647],"height:0.1744em;",[574,3092],{},[574,3094],{"className":3095,"style":837},[836],[574,3097,752],{"className":3098},[841],[574,3100],{"className":3101,"style":837},[836],[574,3103,3105,3108],{"className":3104},[622],[574,3106],{"className":3107,"style":723},[626],[574,3109,2773],{"className":3110},[631],[560,3112,3114],{"id":3113},"typische-fehler","Typische Fehler",[3116,3117,3118,3469,3711],"ul",{},[3119,3120,3121,3122,3221,3222,3257,3258,3440,3441,1037],"li",{},"Negative Koordinaten falsch quadrieren: ",[574,3123,3125,3153],{"className":3124},[577],[574,3126,3128],{"className":3127},[581],[583,3129,3130],{"xmlns":585},[587,3131,3132,3150],{},[590,3133,3134,3136,3138,3140,3146,3148],{},[605,3135,1124],{"stretchy":1123},[605,3137,1315],{},[709,3139,765],{},[1585,3141,3142,3144],{},[605,3143,1134],{"stretchy":1123},[709,3145,768],{},[605,3147,752],{},[709,3149,765],{},[611,3151,3152],{"encoding":613},"(-1)^2 = 1",[574,3154,3156,3212],{"className":3155,"ariaHidden":600},[618],[574,3157,3159,3163,3166,3169,3172,3203,3206,3209],{"className":3158},[622],[574,3160],{"className":3161,"style":3162},[626],"height:1.0641em;vertical-align:-0.25em;",[574,3164,1124],{"className":3165},[1170],[574,3167,1315],{"className":3168},[631],[574,3170,765],{"className":3171},[631],[574,3173,3175,3178],{"className":3174},[1188],[574,3176,1134],{"className":3177},[1188],[574,3179,3181],{"className":3180},[889],[574,3182,3184],{"className":3183},[639],[574,3185,3187],{"className":3186},[643],[574,3188,3191],{"className":3189,"style":3190},[647],"height:0.8141em;",[574,3192,3194,3197],{"style":3193},"top:-3.063em;margin-right:0.05em;",[574,3195],{"className":3196,"style":906},[655],[574,3198,3200],{"className":3199},[910,911,912,913],[574,3201,768],{"className":3202},[631,913],[574,3204],{"className":3205,"style":837},[836],[574,3207,752],{"className":3208},[841],[574,3210],{"className":3211,"style":837},[836],[574,3213,3215,3218],{"className":3214},[622],[574,3216],{"className":3217,"style":723},[626],[574,3219,765],{"className":3220},[631],", nicht ",[574,3223,3225,3241],{"className":3224},[577],[574,3226,3228],{"className":3227},[581],[583,3229,3230],{"xmlns":585},[587,3231,3232,3238],{},[590,3233,3234,3236],{},[605,3235,1315],{},[709,3237,765],{},[611,3239,3240],{"encoding":613},"-1",[574,3242,3244],{"className":3243,"ariaHidden":600},[618],[574,3245,3247,3251,3254],{"className":3246},[622],[574,3248],{"className":3249,"style":3250},[626],"height:0.7278em;vertical-align:-0.0833em;",[574,3252,1315],{"className":3253},[631],[574,3255,765],{"className":3256},[631],". Sonst erhält man ",[574,3259,3261,3294],{"className":3260},[577],[574,3262,3264],{"className":3263},[581],[583,3265,3266],{"xmlns":585},[587,3267,3268,3291],{},[590,3269,3270,3284,3286],{},[754,3271,3272],{},[590,3273,3274,3276,3278,3280,3282],{},[709,3275,1621],{},[605,3277,1315],{},[709,3279,765],{},[605,3281,771],{},[709,3283,1621],{},[605,3285,752],{},[754,3287,3288],{},[709,3289,3290],{},"7",[611,3292,3293],{"encoding":613},"\\sqrt{4 - 1 + 4} = \\sqrt{7}",[574,3295,3297,3383],{"className":3296,"ariaHidden":600},[618],[574,3298,3300,3303,3374,3377,3380],{"className":3299},[622],[574,3301],{"className":3302,"style":3030},[626],[574,3304,3306],{"className":3305},[631,855],[574,3307,3309,3366],{"className":3308},[639,859],[574,3310,3312,3363],{"className":3311},[643],[574,3313,3315,3351],{"className":3314,"style":3043},[647],[574,3316,3318,3321],{"className":3317,"style":651},[870],[574,3319],{"className":3320,"style":656},[655],[574,3322,3324,3327,3330,3333,3336,3339,3342,3345,3348],{"className":3323,"style":1912},[631],[574,3325,1621],{"className":3326},[631],[574,3328],{"className":3329,"style":946},[836],[574,3331,1315],{"className":3332},[950],[574,3334],{"className":3335,"style":946},[836],[574,3337,765],{"className":3338},[631],[574,3340],{"className":3341,"style":946},[836],[574,3343,771],{"className":3344},[950],[574,3346],{"className":3347,"style":946},[836],[574,3349,1621],{"className":3350},[631],[574,3352,3353,3356],{"style":3070},[574,3354],{"className":3355,"style":656},[655],[574,3357,3359],{"className":3358,"style":1949},[1014],[677,3360,3361],{"xmlns":679,"width":1018,"height":1952,"viewBox":1953,"preserveAspectRatio":1021},[686,3362],{"d":1956},[574,3364,933],{"className":3365},[932],[574,3367,3369],{"className":3368},[643],[574,3370,3372],{"className":3371,"style":3090},[647],[574,3373],{},[574,3375],{"className":3376,"style":837},[836],[574,3378,752],{"className":3379},[841],[574,3381],{"className":3382,"style":837},[836],[574,3384,3386,3390],{"className":3385},[622],[574,3387],{"className":3388,"style":3389},[626],"height:1.04em;vertical-align:-0.1328em;",[574,3391,3393],{"className":3392},[631,855],[574,3394,3396,3431],{"className":3395},[639,859],[574,3397,3399,3428],{"className":3398},[643],[574,3400,3403,3415],{"className":3401,"style":3402},[647],"height:0.9072em;",[574,3404,3406,3409],{"className":3405,"style":651},[870],[574,3407],{"className":3408,"style":656},[655],[574,3410,3412],{"className":3411,"style":1912},[631],[574,3413,3290],{"className":3414},[631],[574,3416,3418,3421],{"style":3417},"top:-2.8672em;",[574,3419],{"className":3420,"style":656},[655],[574,3422,3424],{"className":3423,"style":1949},[1014],[677,3425,3426],{"xmlns":679,"width":1018,"height":1952,"viewBox":1953,"preserveAspectRatio":1021},[686,3427],{"d":1956},[574,3429,933],{"className":3430},[932],[574,3432,3434],{"className":3433},[643],[574,3435,3438],{"className":3436,"style":3437},[647],"height:0.1328em;",[574,3439],{}," statt ",[574,3442,3444,3457],{"className":3443},[577],[574,3445,3447],{"className":3446},[581],[583,3448,3449],{"xmlns":585},[587,3450,3451,3455],{},[590,3452,3453],{},[709,3454,1641],{},[611,3456,1641],{"encoding":613},[574,3458,3460],{"className":3459,"ariaHidden":600},[618],[574,3461,3463,3466],{"className":3462},[622],[574,3464],{"className":3465,"style":723},[626],[574,3467,1641],{"className":3468},[631],[3119,3470,3471,3472,3710],{},"Die Wurzel vergessen. ",[574,3473,3475,3515],{"className":3474},[577],[574,3476,3478],{"className":3477},[581],[583,3479,3480],{"xmlns":585},[587,3481,3482,3512],{},[590,3483,3484,3492,3494,3502,3504],{},[759,3485,3486,3488,3490],{},[593,3487,603],{},[709,3489,765],{},[709,3491,768],{},[605,3493,771],{},[759,3495,3496,3498,3500],{},[593,3497,603],{},[709,3499,768],{},[709,3501,768],{},[605,3503,771],{},[759,3505,3506,3508,3510],{},[593,3507,603],{},[709,3509,1641],{},[709,3511,768],{},[611,3513,3514],{"encoding":613},"a_1^2 + a_2^2 + a_3^2",[574,3516,3518,3587,3653],{"className":3517,"ariaHidden":600},[618],[574,3519,3521,3525,3578,3581,3584],{"className":3520},[622],[574,3522],{"className":3523,"style":3524},[626],"height:1.0622em;vertical-align:-0.2481em;",[574,3526,3528,3531],{"className":3527},[631],[574,3529,603],{"className":3530},[631,660],[574,3532,3534],{"className":3533},[889],[574,3535,3537,3569],{"className":3536},[639,859],[574,3538,3540,3566],{"className":3539},[643],[574,3541,3543,3555],{"className":3542,"style":3190},[647],[574,3544,3546,3549],{"style":3545},"top:-2.4519em;margin-left:0em;margin-right:0.05em;",[574,3547],{"className":3548,"style":906},[655],[574,3550,3552],{"className":3551},[910,911,912,913],[574,3553,765],{"className":3554},[631,913],[574,3556,3557,3560],{"style":3193},[574,3558],{"className":3559,"style":906},[655],[574,3561,3563],{"className":3562},[910,911,912,913],[574,3564,768],{"className":3565},[631,913],[574,3567,933],{"className":3568},[932],[574,3570,3572],{"className":3571},[643],[574,3573,3576],{"className":3574,"style":3575},[647],"height:0.2481em;",[574,3577],{},[574,3579],{"className":3580,"style":946},[836],[574,3582,771],{"className":3583},[950],[574,3585],{"className":3586,"style":946},[836],[574,3588,3590,3593,3644,3647,3650],{"className":3589},[622],[574,3591],{"className":3592,"style":3524},[626],[574,3594,3596,3599],{"className":3595},[631],[574,3597,603],{"className":3598},[631,660],[574,3600,3602],{"className":3601},[889],[574,3603,3605,3636],{"className":3604},[639,859],[574,3606,3608,3633],{"className":3607},[643],[574,3609,3611,3622],{"className":3610,"style":3190},[647],[574,3612,3613,3616],{"style":3545},[574,3614],{"className":3615,"style":906},[655],[574,3617,3619],{"className":3618},[910,911,912,913],[574,3620,768],{"className":3621},[631,913],[574,3623,3624,3627],{"style":3193},[574,3625],{"className":3626,"style":906},[655],[574,3628,3630],{"className":3629},[910,911,912,913],[574,3631,768],{"className":3632},[631,913],[574,3634,933],{"className":3635},[932],[574,3637,3639],{"className":3638},[643],[574,3640,3642],{"className":3641,"style":3575},[647],[574,3643],{},[574,3645],{"className":3646,"style":946},[836],[574,3648,771],{"className":3649},[950],[574,3651],{"className":3652,"style":946},[836],[574,3654,3656,3659],{"className":3655},[622],[574,3657],{"className":3658,"style":3524},[626],[574,3660,3662,3665],{"className":3661},[631],[574,3663,603],{"className":3664},[631,660],[574,3666,3668],{"className":3667},[889],[574,3669,3671,3702],{"className":3670},[639,859],[574,3672,3674,3699],{"className":3673},[643],[574,3675,3677,3688],{"className":3676,"style":3190},[647],[574,3678,3679,3682],{"style":3545},[574,3680],{"className":3681,"style":906},[655],[574,3683,3685],{"className":3684},[910,911,912,913],[574,3686,1641],{"className":3687},[631,913],[574,3689,3690,3693],{"style":3193},[574,3691],{"className":3692,"style":906},[655],[574,3694,3696],{"className":3695},[910,911,912,913],[574,3697,768],{"className":3698},[631,913],[574,3700,933],{"className":3701},[932],[574,3703,3705],{"className":3704},[643],[574,3706,3708],{"className":3707,"style":3575},[647],[574,3709],{}," ist das Quadrat der Länge.",[3119,3712,3713,3714,3807,3808,3221,3836,1037],{},"Die Wurzel gliedweise ziehen: ",[574,3715,3717,3739],{"className":3716},[577],[574,3718,3720],{"className":3719},[581],[583,3721,3722],{"xmlns":585},[587,3723,3724,3736],{},[590,3725,3726],{},[754,3727,3728],{},[590,3729,3730,3732,3734],{},[709,3731,1636],{},[605,3733,771],{},[709,3735,2841],{},[611,3737,3738],{"encoding":613},"\\sqrt{9 + 16}",[574,3740,3742],{"className":3741,"ariaHidden":600},[618],[574,3743,3745,3748],{"className":3744},[622],[574,3746],{"className":3747,"style":3030},[626],[574,3749,3751],{"className":3750},[631,855],[574,3752,3754,3799],{"className":3753},[639,859],[574,3755,3757,3796],{"className":3756},[643],[574,3758,3760,3784],{"className":3759,"style":3043},[647],[574,3761,3763,3766],{"className":3762,"style":651},[870],[574,3764],{"className":3765,"style":656},[655],[574,3767,3769,3772,3775,3778,3781],{"className":3768,"style":1912},[631],[574,3770,1636],{"className":3771},[631],[574,3773],{"className":3774,"style":946},[836],[574,3776,771],{"className":3777},[950],[574,3779],{"className":3780,"style":946},[836],[574,3782,2841],{"className":3783},[631],[574,3785,3786,3789],{"style":3070},[574,3787],{"className":3788,"style":656},[655],[574,3790,3792],{"className":3791,"style":1949},[1014],[677,3793,3794],{"xmlns":679,"width":1018,"height":1952,"viewBox":1953,"preserveAspectRatio":1021},[686,3795],{"d":1956},[574,3797,933],{"className":3798},[932],[574,3800,3802],{"className":3801},[643],[574,3803,3805],{"className":3804,"style":3090},[647],[574,3806],{}," ist ",[574,3809,3811,3824],{"className":3810},[577],[574,3812,3814],{"className":3813},[581],[583,3815,3816],{"xmlns":585},[587,3817,3818,3822],{},[590,3819,3820],{},[709,3821,2773],{},[611,3823,2773],{"encoding":613},[574,3825,3827],{"className":3826,"ariaHidden":600},[618],[574,3828,3830,3833],{"className":3829},[622],[574,3831],{"className":3832,"style":723},[626],[574,3834,2773],{"className":3835},[631],[574,3837,3839,3861],{"className":3838},[577],[574,3840,3842],{"className":3841},[581],[583,3843,3844],{"xmlns":585},[587,3845,3846,3858],{},[590,3847,3848,3850,3852,3854,3856],{},[709,3849,1641],{},[605,3851,771],{},[709,3853,1621],{},[605,3855,752],{},[709,3857,3290],{},[611,3859,3860],{"encoding":613},"3 + 4 = 7",[574,3862,3864,3882,3900],{"className":3863,"ariaHidden":600},[618],[574,3865,3867,3870,3873,3876,3879],{"className":3866},[622],[574,3868],{"className":3869,"style":3250},[626],[574,3871,1641],{"className":3872},[631],[574,3874],{"className":3875,"style":946},[836],[574,3877,771],{"className":3878},[950],[574,3880],{"className":3881,"style":946},[836],[574,3883,3885,3888,3891,3894,3897],{"className":3884},[622],[574,3886],{"className":3887,"style":723},[626],[574,3889,1621],{"className":3890},[631],[574,3892],{"className":3893,"style":837},[836],[574,3895,752],{"className":3896},[841],[574,3898],{"className":3899,"style":837},[836],[574,3901,3903,3906],{"className":3902},[622],[574,3904],{"className":3905,"style":723},[626],[574,3907,3290],{"className":3908},[631],{"title":3910,"searchDepth":3911,"depth":3911,"links":3912},"",2,[3913,3914,3915],{"id":562,"depth":3911,"text":563},{"id":1259,"depth":3911,"text":1260},{"id":3113,"depth":3911,"text":3114},[3917,3920,3922,3924,3927,3930,3932],{"lhs":3918,"rhs":3919},"sqrt(a1^2 + a2^2 + a3^2)","norm([a1, a2, a3])",{"lhs":3918,"rhs":3921},"sqrt((-a1)^2 + (-a2)^2 + (-a3)^2)",{"lhs":3923,"rhs":1641},"sqrt(2^2 + (-1)^2 + 2^2)",{"lhs":3925,"rhs":3926},"sqrt(3^2 + (-2)^2 + 4^2)","sqrt(29)",{"lhs":3928,"rhs":3929},"round(sqrt(29), 2)","5.39",{"lhs":3931,"rhs":2773},"sqrt(3^2 + 4^2)",{"lhs":3933,"rhs":3934},"sqrt(2^2 - 1 + 2^2)","sqrt(7)",null,"md","vector-length","|\\vec{a}| = \\sqrt{a_1^2 + a_2^2 + a_3^2}","\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>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmsqrt>\u003Cmrow>\u003Cmsubsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsubsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsubsup>\u003Cmo>+\u003C\u002Fmo>\u003Cmsubsup>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsubsup>\u003C\u002Fmrow>\u003C\u002Fmsqrt>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">|\\vec{a}| = \\sqrt{a_1^2 + a_2^2 + a_3^2}\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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=\"mord\">∣\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:1.84em;vertical-align:-0.5413em;\">\u003C\u002Fspan>\u003Cspan class=\"mord sqrt\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.2987em;\">\u003Cspan class=\"svg-align\" style=\"top:-3.8em;\">\u003Cspan class=\"pstrut\" style=\"height:3.8em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\" style=\"padding-left:1em;\">\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7959em;\">\u003Cspan style=\"top:-2.4337em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.0448em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\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:0.2663em;\">\u003Cspan>\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\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7959em;\">\u003Cspan style=\"top:-2.4337em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.0448em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\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:0.2663em;\">\u003Cspan>\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\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7959em;\">\u003Cspan style=\"top:-2.4337em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.0448em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\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:0.2663em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2587em;\">\u003Cspan class=\"pstrut\" style=\"height:3.8em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"min-width:1.02em;height:1.88em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"1.88em\" viewBox=\"0 0 400000 1944\" preserveAspectRatio=\"xMinYMin slice\">\u003Cpath d=\"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.5413em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fbetrag-eines-vektors",[],[3946,3947,3948,3949],"vector-between-points","unit-vector","dot-product","pythagorean-theorem",{"title":548,"description":3910},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fbetrag-eines-vektors","Die Länge eines Vektors ist die Wurzel aus der Summe der Quadrate seiner Koordinaten.",[3954,3955,3956,3957,3958],"vektor","länge","betrag","abstand","analytische geometrie",[3960,3964,3968],{"symbol":3961,"meaning":3962,"symbolHtml":3963},"\\vec{a}","Vektor mit den Koordinaten a₁, a₂, a₃","\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>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{a}\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\">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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3965,"meaning":3966,"symbolHtml":3967},"a_1, a_2, a_3","Koordinaten des Vektors","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_1, a_2, a_3\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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">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:0.15em;\">\u003Cspan>\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\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\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:0.15em;\">\u003Cspan>\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\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">3\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":614,"meaning":3969,"symbolHtml":3970},"Betrag, also die Länge des Pfeils","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">|\\vec{a}|\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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=\"mord\">∣\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","l11loKVSPZh_ZuU8MktcQKd8kJopVOySEnERea2RwHo",[3973,3976,3979,3982],{"stem":3974,"title":3975,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fsatz-des-pythagoras","Satz des Pythagoras",{"stem":3977,"title":3978,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Feinheitsvektor","Einheitsvektor",{"stem":3980,"title":3981,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fskalarprodukt","Skalarprodukt",{"stem":3983,"title":3984,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fverbindungsvektor","Verbindungsvektor",1793824277290]