[{"data":1,"prerenderedAt":4058},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fparameterform-gerade":546,"formula-related-de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fparameterform-gerade":4045},[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":3972,"conditions":4001,"conditionsHtml":4002,"deprecated":4003,"description":3966,"extension":4004,"figure":4003,"figureCaption":4003,"figureHtml":4003,"formulaId":4005,"latex":4006,"latexHtml":4007,"level":4008,"meta":4009,"navigation":4010,"path":4011,"redirectFrom":4012,"related":4013,"seo":4018,"stem":4019,"subject":578,"summary":4020,"tags":4021,"variables":4027,"__hash__":4044},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fparameterform-gerade.md","Parameterform einer Geraden",[550,551,552,553,554,555],"Geradengleichung im Raum","Gerade durch zwei Punkte Vektor","Punktrichtungsform","Stützvektor und Richtungsvektor","Vektorgleichung einer Geraden","Punktprobe Gerade",{"type":557,"value":558,"toc":3965},"minimark",[559,564,679,1002,1534,1572,1576,1925,2475,2640,3153,3700,3704],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,568,678],"p",{},"Eine Gerade im Raum lässt sich nicht wie in der Ebene als ",[569,570,573,612],"span",{"className":571},[572],"katex",[569,574,577],{"className":575},[576],"katex-mathml",[578,579,581],"math",{"xmlns":580},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[582,583,584,607],"semantics",{},[585,586,587,591,595,598,601,604],"mrow",{},[588,589,590],"mi",{},"y",[592,593,594],"mo",{},"=",[588,596,597],{},"m",[588,599,600],{},"x",[592,602,603],{},"+",[588,605,606],{},"b",[608,609,611],"annotation",{"encoding":610},"application\u002Fx-tex","y = mx + b",[569,613,617,644,668],{"className":614,"ariaHidden":616},[615],"katex-html","true",[569,618,621,626,632,637,641],{"className":619},[620],"base",[569,622],{"className":623,"style":625},[624],"strut","height:0.625em;vertical-align:-0.1944em;",[569,627,590],{"className":628,"style":631},[629,630],"mord","mathnormal","margin-right:0.0359em;",[569,633],{"className":634,"style":636},[635],"mspace","margin-right:0.2778em;",[569,638,594],{"className":639},[640],"mrel",[569,642],{"className":643,"style":636},[635],[569,645,647,651,654,657,661,665],{"className":646},[620],[569,648],{"className":649,"style":650},[624],"height:0.6667em;vertical-align:-0.0833em;",[569,652,597],{"className":653},[629,630],[569,655,600],{"className":656},[629,630],[569,658],{"className":659,"style":660},[635],"margin-right:0.2222em;",[569,662,603],{"className":663},[664],"mbin",[569,666],{"className":667,"style":660},[635],[569,669,671,675],{"className":670},[620],[569,672],{"className":673,"style":674},[624],"height:0.6944em;",[569,676,606],{"className":677},[629,630]," schreiben. Stattdessen beschreibt man sie mit Vektoren:",[680,681,682,796,869],"ul",{},[683,684,685,686,690,691,795],"li",{},"Der ",[687,688,689],"strong",{},"Stützvektor"," ",[569,692,694,714],{"className":693},[572],[569,695,697],{"className":696},[576],[578,698,699],{"xmlns":580},[582,700,701,711],{},[585,702,703],{},[704,705,706,708],"mover",{"accent":616},[588,707,565],{},[592,709,710],{},"⃗",[608,712,713],{"encoding":610},"\\vec{p}",[569,715,717],{"className":716,"ariaHidden":616},[615],[569,718,720,724],{"className":719},[620],[569,721],{"className":722,"style":723},[624],"height:0.9084em;vertical-align:-0.1944em;",[569,725,728],{"className":726},[629,727],"accent",[569,729,733,786],{"className":730},[731,732],"vlist-t","vlist-t2",[569,734,737,781],{"className":735},[736],"vlist-r",[569,738,742,753],{"className":739,"style":741},[740],"vlist","height:0.714em;",[569,743,745,750],{"style":744},"top:-3em;",[569,746],{"className":747,"style":749},[748],"pstrut","height:3em;",[569,751,565],{"className":752},[629,630],[569,754,755,758],{"style":744},[569,756],{"className":757,"style":749},[748],[569,759,763],{"className":760,"style":762},[761],"accent-body","left:-0.1522em;",[569,764,768],{"className":765,"style":767},[766],"overlay","height:0.714em;width:0.471em;",[769,770,777],"svg",{"xmlns":771,"width":772,"height":773,"style":774,"viewBox":775,"preserveAspectRatio":776},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","0.471em","0.714em","width:0.471em","0 0 471 714","xMinYMin",[778,779],"path",{"d":780},"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",[569,782,785],{"className":783},[784],"vlist-s","​",[569,787,789],{"className":788},[736],[569,790,793],{"className":791,"style":792},[740],"height:0.1944em;",[569,794],{}," führt vom Ursprung zu einem Punkt der Geraden.",[683,797,685,798,690,801,868],{},[687,799,800],{},"Richtungsvektor",[569,802,804,823],{"className":803},[572],[569,805,807],{"className":806},[576],[578,808,809],{"xmlns":580},[582,810,811,820],{},[585,812,813],{},[704,814,815,818],{"accent":616},[588,816,817],{},"u",[592,819,710],{},[608,821,822],{"encoding":610},"\\vec{u}",[569,824,826],{"className":825,"ariaHidden":616},[615],[569,827,829,832],{"className":828},[620],[569,830],{"className":831,"style":741},[624],[569,833,835],{"className":834},[629,727],[569,836,838],{"className":837},[731],[569,839,841],{"className":840},[736],[569,842,844,852],{"className":843,"style":741},[740],[569,845,846,849],{"style":744},[569,847],{"className":848,"style":749},[748],[569,850,817],{"className":851},[629,630],[569,853,854,857],{"style":744},[569,855],{"className":856,"style":749},[748],[569,858,861],{"className":859,"style":860},[761],"left:-0.2077em;",[569,862,864],{"className":863,"style":767},[766],[769,865,866],{"xmlns":771,"width":772,"height":773,"style":774,"viewBox":775,"preserveAspectRatio":776},[778,867],{"d":780}," gibt an, in welche Richtung die Gerade verläuft.",[683,870,685,871,690,874,904,905,936,937,1001],{},[687,872,873],{},"Parameter",[569,875,877,891],{"className":876},[572],[569,878,880],{"className":879},[576],[578,881,882],{"xmlns":580},[582,883,884,889],{},[585,885,886],{},[588,887,888],{},"t",[608,890,888],{"encoding":610},[569,892,894],{"className":893,"ariaHidden":616},[615],[569,895,897,901],{"className":896},[620],[569,898],{"className":899,"style":900},[624],"height:0.6151em;",[569,902,888],{"className":903},[629,630]," legt fest, wie weit man von ",[569,906,908,922],{"className":907},[572],[569,909,911],{"className":910},[576],[578,912,913],{"xmlns":580},[582,914,915,920],{},[585,916,917],{},[588,918,919],{},"P",[608,921,919],{"encoding":610},[569,923,925],{"className":924,"ariaHidden":616},[615],[569,926,928,932],{"className":927},[620],[569,929],{"className":930,"style":931},[624],"height:0.6833em;",[569,933,919],{"className":934,"style":935},[629,630],"margin-right:0.1389em;"," aus in Richtung ",[569,938,940,957],{"className":939},[572],[569,941,943],{"className":942},[576],[578,944,945],{"xmlns":580},[582,946,947,955],{},[585,948,949],{},[704,950,951,953],{"accent":616},[588,952,817],{},[592,954,710],{},[608,956,822],{"encoding":610},[569,958,960],{"className":959,"ariaHidden":616},[615],[569,961,963,966],{"className":962},[620],[569,964],{"className":965,"style":741},[624],[569,967,969],{"className":968},[629,727],[569,970,972],{"className":971},[731],[569,973,975],{"className":974},[736],[569,976,978,986],{"className":977,"style":741},[740],[569,979,980,983],{"style":744},[569,981],{"className":982,"style":749},[748],[569,984,817],{"className":985},[629,630],[569,987,988,991],{"style":744},[569,989],{"className":990,"style":749},[748],[569,992,994],{"className":993,"style":860},[761],[569,995,997],{"className":996,"style":767},[766],[769,998,999],{"xmlns":771,"width":772,"height":773,"style":774,"viewBox":775,"preserveAspectRatio":776},[778,1000],{"d":780}," geht. Negative Werte führen in die Gegenrichtung.",[565,1003,1004,1005,1034,1035,1065,1066,1034,1202,1344,1345,1435,1436,1533],{},"Für die Gerade durch zwei Punkte ",[569,1006,1008,1022],{"className":1007},[572],[569,1009,1011],{"className":1010},[576],[578,1012,1013],{"xmlns":580},[582,1014,1015,1020],{},[585,1016,1017],{},[588,1018,1019],{},"A",[608,1021,1019],{"encoding":610},[569,1023,1025],{"className":1024,"ariaHidden":616},[615],[569,1026,1028,1031],{"className":1027},[620],[569,1029],{"className":1030,"style":931},[624],[569,1032,1019],{"className":1033},[629,630]," und ",[569,1036,1038,1052],{"className":1037},[572],[569,1039,1041],{"className":1040},[576],[578,1042,1043],{"xmlns":580},[582,1044,1045,1050],{},[585,1046,1047],{},[588,1048,1049],{},"B",[608,1051,1049],{"encoding":610},[569,1053,1055],{"className":1054,"ariaHidden":616},[615],[569,1056,1058,1061],{"className":1057},[620],[569,1059],{"className":1060,"style":931},[624],[569,1062,1049],{"className":1063,"style":1064},[629,630],"margin-right:0.0502em;"," nimmt man ",[569,1067,1069,1096],{"className":1068},[572],[569,1070,1072],{"className":1071},[576],[578,1073,1074],{"xmlns":580},[582,1075,1076,1093],{},[585,1077,1078,1084,1086],{},[704,1079,1080,1082],{"accent":616},[588,1081,565],{},[592,1083,710],{},[592,1085,594],{},[704,1087,1088,1091],{"accent":616},[588,1089,1090],{},"a",[592,1092,710],{},[608,1094,1095],{"encoding":610},"\\vec{p} = \\vec{a}",[569,1097,1099,1160],{"className":1098,"ariaHidden":616},[615],[569,1100,1102,1105,1151,1154,1157],{"className":1101},[620],[569,1103],{"className":1104,"style":723},[624],[569,1106,1108],{"className":1107},[629,727],[569,1109,1111,1143],{"className":1110},[731,732],[569,1112,1114,1140],{"className":1113},[736],[569,1115,1117,1125],{"className":1116,"style":741},[740],[569,1118,1119,1122],{"style":744},[569,1120],{"className":1121,"style":749},[748],[569,1123,565],{"className":1124},[629,630],[569,1126,1127,1130],{"style":744},[569,1128],{"className":1129,"style":749},[748],[569,1131,1133],{"className":1132,"style":762},[761],[569,1134,1136],{"className":1135,"style":767},[766],[769,1137,1138],{"xmlns":771,"width":772,"height":773,"style":774,"viewBox":775,"preserveAspectRatio":776},[778,1139],{"d":780},[569,1141,785],{"className":1142},[784],[569,1144,1146],{"className":1145},[736],[569,1147,1149],{"className":1148,"style":792},[740],[569,1150],{},[569,1152],{"className":1153,"style":636},[635],[569,1155,594],{"className":1156},[640],[569,1158],{"className":1159,"style":636},[635],[569,1161,1163,1166],{"className":1162},[620],[569,1164],{"className":1165,"style":741},[624],[569,1167,1169],{"className":1168},[629,727],[569,1170,1172],{"className":1171},[731],[569,1173,1175],{"className":1174},[736],[569,1176,1178,1186],{"className":1177,"style":741},[740],[569,1179,1180,1183],{"style":744},[569,1181],{"className":1182,"style":749},[748],[569,1184,1090],{"className":1185},[629,630],[569,1187,1188,1191],{"style":744},[569,1189],{"className":1190,"style":749},[748],[569,1192,1195],{"className":1193,"style":1194},[761],"left:-0.2355em;",[569,1196,1198],{"className":1197,"style":767},[766],[769,1199,1200],{"xmlns":771,"width":772,"height":773,"style":774,"viewBox":775,"preserveAspectRatio":776},[778,1201],{"d":780},[569,1203,1205,1236],{"className":1204},[572],[569,1206,1208],{"className":1207},[576],[578,1209,1210],{"xmlns":580},[582,1211,1212,1233],{},[585,1213,1214,1220,1222],{},[704,1215,1216,1218],{"accent":616},[588,1217,817],{},[592,1219,710],{},[592,1221,594],{},[704,1223,1224,1230],{"accent":616},[585,1225,1226,1228],{},[588,1227,1019],{},[588,1229,1049],{},[592,1231,1232],{"stretchy":616},"→",[608,1234,1235],{"encoding":610},"\\vec{u} = \\overrightarrow{AB}",[569,1237,1239,1289],{"className":1238,"ariaHidden":616},[615],[569,1240,1242,1245,1280,1283,1286],{"className":1241},[620],[569,1243],{"className":1244,"style":741},[624],[569,1246,1248],{"className":1247},[629,727],[569,1249,1251],{"className":1250},[731],[569,1252,1254],{"className":1253},[736],[569,1255,1257,1265],{"className":1256,"style":741},[740],[569,1258,1259,1262],{"style":744},[569,1260],{"className":1261,"style":749},[748],[569,1263,817],{"className":1264},[629,630],[569,1266,1267,1270],{"style":744},[569,1268],{"className":1269,"style":749},[748],[569,1271,1273],{"className":1272,"style":860},[761],[569,1274,1276],{"className":1275,"style":767},[766],[769,1277,1278],{"xmlns":771,"width":772,"height":773,"style":774,"viewBox":775,"preserveAspectRatio":776},[778,1279],{"d":780},[569,1281],{"className":1282,"style":636},[635],[569,1284,594],{"className":1285},[640],[569,1287],{"className":1288,"style":636},[635],[569,1290,1292,1296],{"className":1291},[620],[569,1293],{"className":1294,"style":1295},[624],"height:1.2053em;",[569,1297,1299],{"className":1298},[629,727],[569,1300,1302],{"className":1301},[731],[569,1303,1305],{"className":1304},[736],[569,1306,1308,1322],{"className":1307,"style":1295},[740],[569,1309,1310,1313],{"style":744},[569,1311],{"className":1312,"style":749},[748],[569,1314,1316,1319],{"className":1315},[629],[569,1317,1019],{"className":1318},[629,630],[569,1320,1049],{"className":1321,"style":1064},[629,630],[569,1323,1327,1330],{"className":1324,"style":1326},[1325],"svg-align","top:-3.6833em;",[569,1328],{"className":1329,"style":749},[748],[569,1331,1335],{"className":1332,"style":1334},[1333],"hide-tail","height:0.522em;min-width:0.888em;",[769,1336,1341],{"xmlns":771,"width":1337,"height":1338,"viewBox":1339,"preserveAspectRatio":1340},"400em","0.522em","0 0 400000 522","xMaxYMin slice",[778,1342],{"d":1343},"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",". Die Darstellung ist nicht eindeutig: Jeder andere Punkt der Geraden taugt als Stützpunkt, jedes Vielfache ",[569,1346,1348,1372],{"className":1347},[572],[569,1349,1351],{"className":1350},[576],[578,1352,1353],{"xmlns":580},[582,1354,1355,1369],{},[585,1356,1357,1360,1363],{},[588,1358,1359],{},"k",[592,1361,1362],{},"⋅",[704,1364,1365,1367],{"accent":616},[588,1366,817],{},[592,1368,710],{},[608,1370,1371],{"encoding":610},"k \\cdot \\vec{u}",[569,1373,1375,1394],{"className":1374,"ariaHidden":616},[615],[569,1376,1378,1381,1385,1388,1391],{"className":1377},[620],[569,1379],{"className":1380,"style":674},[624],[569,1382,1359],{"className":1383,"style":1384},[629,630],"margin-right:0.0315em;",[569,1386],{"className":1387,"style":660},[635],[569,1389,1362],{"className":1390},[664],[569,1392],{"className":1393,"style":660},[635],[569,1395,1397,1400],{"className":1396},[620],[569,1398],{"className":1399,"style":741},[624],[569,1401,1403],{"className":1402},[629,727],[569,1404,1406],{"className":1405},[731],[569,1407,1409],{"className":1408},[736],[569,1410,1412,1420],{"className":1411,"style":741},[740],[569,1413,1414,1417],{"style":744},[569,1415],{"className":1416,"style":749},[748],[569,1418,817],{"className":1419},[629,630],[569,1421,1422,1425],{"style":744},[569,1423],{"className":1424,"style":749},[748],[569,1426,1428],{"className":1427,"style":860},[761],[569,1429,1431],{"className":1430,"style":767},[766],[769,1432,1433],{"xmlns":771,"width":772,"height":773,"style":774,"viewBox":775,"preserveAspectRatio":776},[778,1434],{"d":780}," mit ",[569,1437,1439,1461],{"className":1438},[572],[569,1440,1442],{"className":1441},[576],[578,1443,1444],{"xmlns":580},[582,1445,1446,1458],{},[585,1447,1448,1450,1454],{},[588,1449,1359],{},[592,1451,1453],{"mathvariant":1452},"normal","≠",[1455,1456,1457],"mn",{},"0",[608,1459,1460],{"encoding":610},"k \\neq 0",[569,1462,1464,1523],{"className":1463,"ariaHidden":616},[615],[569,1465,1467,1471,1474,1477,1520],{"className":1466},[620],[569,1468],{"className":1469,"style":1470},[624],"height:0.8889em;vertical-align:-0.1944em;",[569,1472,1359],{"className":1473,"style":1384},[629,630],[569,1475],{"className":1476,"style":636},[635],[569,1478,1480,1513,1517],{"className":1479},[640],[569,1481,1483],{"className":1482},[640],[569,1484,1487],{"className":1485},[629,1486],"vbox",[569,1488,1491],{"className":1489},[1490],"thinbox",[569,1492,1495,1498,1509],{"className":1493},[1494],"rlap",[569,1496],{"className":1497,"style":1470},[624],[569,1499,1502],{"className":1500},[1501],"inner",[569,1503,1505],{"className":1504},[629],[569,1506,1508],{"className":1507},[640],"",[569,1510],{"className":1511},[1512],"fix",[569,1514],{"className":1515},[635,1516],"nobreak",[569,1518,594],{"className":1519},[640],[569,1521],{"className":1522,"style":636},[635],[569,1524,1526,1530],{"className":1525},[620],[569,1527],{"className":1528,"style":1529},[624],"height:0.6444em;",[569,1531,1457],{"className":1532},[629]," als Richtungsvektor.",[565,1535,1536,1539,1540,690,1543,1571],{},[687,1537,1538],{},"Punktprobe",": Ein Punkt liegt auf der Geraden, wenn es ",[687,1541,1542],{},"ein",[569,1544,1546,1559],{"className":1545},[572],[569,1547,1549],{"className":1548},[576],[578,1550,1551],{"xmlns":580},[582,1552,1553,1557],{},[585,1554,1555],{},[588,1556,888],{},[608,1558,888],{"encoding":610},[569,1560,1562],{"className":1561,"ariaHidden":616},[615],[569,1563,1565,1568],{"className":1564},[620],[569,1566],{"className":1567,"style":900},[624],[569,1569,888],{"className":1570},[629,630]," gibt, das alle drei Koordinatengleichungen gleichzeitig erfüllt.",[560,1573,1575],{"id":1574},"beispiele","Beispiele",[565,1577,1578,1579,1034,1676,1772,1773,1924],{},"Gerade durch ",[569,1580,1582,1616],{"className":1581},[572],[569,1583,1585],{"className":1584},[576],[578,1586,1587],{"xmlns":580},[582,1588,1589,1613],{},[585,1590,1591,1593,1597,1600,1603,1606,1608,1610],{},[588,1592,1019],{},[592,1594,1596],{"stretchy":1595},"false","(",[1455,1598,1599],{},"1",[592,1601,1602],{},"∣",[1455,1604,1605],{},"2",[592,1607,1602],{},[1455,1609,1457],{},[592,1611,1612],{"stretchy":1595},")",[608,1614,1615],{"encoding":610},"A(1 \\mid 2 \\mid 0)",[569,1617,1619,1645,1663],{"className":1618,"ariaHidden":616},[615],[569,1620,1622,1626,1629,1633,1636,1639,1642],{"className":1621},[620],[569,1623],{"className":1624,"style":1625},[624],"height:1em;vertical-align:-0.25em;",[569,1627,1019],{"className":1628},[629,630],[569,1630,1596],{"className":1631},[1632],"mopen",[569,1634,1599],{"className":1635},[629],[569,1637],{"className":1638,"style":636},[635],[569,1640,1602],{"className":1641},[640],[569,1643],{"className":1644,"style":636},[635],[569,1646,1648,1651,1654,1657,1660],{"className":1647},[620],[569,1649],{"className":1650,"style":1625},[624],[569,1652,1605],{"className":1653},[629],[569,1655],{"className":1656,"style":636},[635],[569,1658,1602],{"className":1659},[640],[569,1661],{"className":1662,"style":636},[635],[569,1664,1666,1669,1672],{"className":1665},[620],[569,1667],{"className":1668,"style":1625},[624],[569,1670,1457],{"className":1671},[629],[569,1673,1612],{"className":1674},[1675],"mclose",[569,1677,1679,1712],{"className":1678},[572],[569,1680,1682],{"className":1681},[576],[578,1683,1684],{"xmlns":580},[582,1685,1686,1709],{},[585,1687,1688,1690,1692,1695,1697,1700,1702,1704,1707],{},[588,1689,1049],{},[592,1691,1596],{"stretchy":1595},[1455,1693,1694],{},"3",[592,1696,1602],{},[592,1698,1699],{},"−",[1455,1701,1599],{},[592,1703,1602],{},[1455,1705,1706],{},"4",[592,1708,1612],{"stretchy":1595},[608,1710,1711],{"encoding":610},"B(3 \\mid -1 \\mid 4)",[569,1713,1715,1739,1760],{"className":1714,"ariaHidden":616},[615],[569,1716,1718,1721,1724,1727,1730,1733,1736],{"className":1717},[620],[569,1719],{"className":1720,"style":1625},[624],[569,1722,1049],{"className":1723,"style":1064},[629,630],[569,1725,1596],{"className":1726},[1632],[569,1728,1694],{"className":1729},[629],[569,1731],{"className":1732,"style":636},[635],[569,1734,1602],{"className":1735},[640],[569,1737],{"className":1738,"style":636},[635],[569,1740,1742,1745,1748,1751,1754,1757],{"className":1741},[620],[569,1743],{"className":1744,"style":1625},[624],[569,1746,1699],{"className":1747},[629],[569,1749,1599],{"className":1750},[629],[569,1752],{"className":1753,"style":636},[635],[569,1755,1602],{"className":1756},[640],[569,1758],{"className":1759,"style":636},[635],[569,1761,1763,1766,1769],{"className":1762},[620],[569,1764],{"className":1765,"style":1625},[624],[569,1767,1706],{"className":1768},[629],[569,1770,1612],{"className":1771},[1675],". Der Richtungsvektor ist ",[569,1774,1776,1823],{"className":1775},[572],[569,1777,1779],{"className":1778},[576],[578,1780,1781],{"xmlns":580},[582,1782,1783,1820],{},[585,1784,1785,1795,1797,1799,1801,1804,1808,1810,1812,1814,1816,1818],{},[704,1786,1787,1793],{"accent":616},[585,1788,1789,1791],{},[588,1790,1019],{},[588,1792,1049],{},[592,1794,1232],{"stretchy":616},[592,1796,594],{},[592,1798,1596],{"stretchy":1595},[1455,1800,1605],{},[592,1802,1803],{"separator":616},",",[1805,1806,1807],"mtext",{}," ",[592,1809,1699],{},[1455,1811,1694],{},[592,1813,1803],{"separator":616},[1805,1815,1807],{},[1455,1817,1706],{},[592,1819,1612],{"stretchy":1595},[608,1821,1822],{"encoding":610},"\\overrightarrow{AB} = (2,\\ -3,\\ 4)",[569,1824,1826,1880],{"className":1825,"ariaHidden":616},[615],[569,1827,1829,1832,1871,1874,1877],{"className":1828},[620],[569,1830],{"className":1831,"style":1295},[624],[569,1833,1835],{"className":1834},[629,727],[569,1836,1838],{"className":1837},[731],[569,1839,1841],{"className":1840},[736],[569,1842,1844,1858],{"className":1843,"style":1295},[740],[569,1845,1846,1849],{"style":744},[569,1847],{"className":1848,"style":749},[748],[569,1850,1852,1855],{"className":1851},[629],[569,1853,1019],{"className":1854},[629,630],[569,1856,1049],{"className":1857,"style":1064},[629,630],[569,1859,1861,1864],{"className":1860,"style":1326},[1325],[569,1862],{"className":1863,"style":749},[748],[569,1865,1867],{"className":1866,"style":1334},[1333],[769,1868,1869],{"xmlns":771,"width":1337,"height":1338,"viewBox":1339,"preserveAspectRatio":1340},[778,1870],{"d":1343},[569,1872],{"className":1873,"style":636},[635],[569,1875,594],{"className":1876},[640],[569,1878],{"className":1879,"style":636},[635],[569,1881,1883,1886,1889,1892,1896,1899,1903,1906,1909,1912,1915,1918,1921],{"className":1882},[620],[569,1884],{"className":1885,"style":1625},[624],[569,1887,1596],{"className":1888},[1632],[569,1890,1605],{"className":1891},[629],[569,1893,1803],{"className":1894},[1895],"mpunct",[569,1897,1807],{"className":1898},[635],[569,1900],{"className":1901,"style":1902},[635],"margin-right:0.1667em;",[569,1904,1699],{"className":1905},[629],[569,1907,1694],{"className":1908},[629],[569,1910,1803],{"className":1911},[1895],[569,1913,1807],{"className":1914},[635],[569,1916],{"className":1917,"style":1902},[635],[569,1919,1706],{"className":1920},[629],[569,1922,1612],{"className":1923},[1675],":",[569,1926,1929],{"className":1927},[1928],"katex-display",[569,1930,1932,2054],{"className":1931},[572],[569,1933,1935],{"className":1934},[576],[578,1936,1938],{"xmlns":580,"display":1937},"block",[582,1939,1940,2051],{},[585,1941,1942,1945,1947,1950,1954,1957,1959,1962,1968,1970,2009,2011,2013,2015],{},[588,1943,1944],{},"g",[635,1946],{},[635,1948],{"width":1949},"0.1111em",[592,1951],{"lspace":1952,"rspace":1953},"0em","0.17em",[1805,1955,1956],{}," ⁣",[592,1958,1924],{"lspace":1952,"rspace":1952},[635,1960],{"width":1961},"0.3333em",[704,1963,1964,1966],{"accent":616},[588,1965,600],{},[592,1967,710],{},[592,1969,594],{},[585,1971,1972,1974,2007],{},[592,1973,1596],{"fence":616},[1975,1976,1980,1991,1999],"mtable",{"rowspacing":1977,"columnalign":1978,"columnspacing":1979},"0.16em","center","1em",[1981,1982,1983],"mtr",{},[1984,1985,1986],"mtd",{},[1987,1988,1989],"mstyle",{"scriptlevel":1457,"displaystyle":1595},[1455,1990,1599],{},[1981,1992,1993],{},[1984,1994,1995],{},[1987,1996,1997],{"scriptlevel":1457,"displaystyle":1595},[1455,1998,1605],{},[1981,2000,2001],{},[1984,2002,2003],{},[1987,2004,2005],{"scriptlevel":1457,"displaystyle":1595},[1455,2006,1457],{},[592,2008,1612],{"fence":616},[592,2010,603],{},[588,2012,888],{},[592,2014,1362],{},[585,2016,2017,2019,2049],{},[592,2018,1596],{"fence":616},[1975,2020,2021,2029,2041],{"rowspacing":1977,"columnalign":1978,"columnspacing":1979},[1981,2022,2023],{},[1984,2024,2025],{},[1987,2026,2027],{"scriptlevel":1457,"displaystyle":1595},[1455,2028,1605],{},[1981,2030,2031],{},[1984,2032,2033],{},[1987,2034,2035],{"scriptlevel":1457,"displaystyle":1595},[585,2036,2037,2039],{},[592,2038,1699],{},[1455,2040,1694],{},[1981,2042,2043],{},[1984,2044,2045],{},[1987,2046,2047],{"scriptlevel":1457,"displaystyle":1595},[1455,2048,1706],{},[592,2050,1612],{"fence":616},[608,2052,2053],{"encoding":610},"g\\colon \\vec{x} = \\begin{pmatrix} 1 \\\\ 2 \\\\ 0 \\end{pmatrix} + t \\cdot \\begin{pmatrix} 2 \\\\ -3 \\\\ 4 \\end{pmatrix}",[569,2055,2057,2137,2309,2327],{"className":2056,"ariaHidden":616},[615],[569,2058,2060,2063,2066,2069,2073,2076,2080,2083,2089,2093,2128,2131,2134],{"className":2059},[620],[569,2061],{"className":2062,"style":723},[624],[569,2064,1944],{"className":2065,"style":631},[629,630],[569,2067],{"className":2068},[635,1516],[569,2070],{"className":2071,"style":2072},[635],"margin-right:0.1111em;",[569,2074],{"className":2075},[1895],[569,2077],{"className":2078,"style":2079},[635],"margin-right:-0.1667em;",[569,2081],{"className":2082,"style":1902},[635],[569,2084,2086],{"className":2085},[629],[569,2087,1924],{"className":2088},[640],[569,2090],{"className":2091,"style":2092},[635],"margin-right:0.3333em;",[569,2094,2096],{"className":2095},[629,727],[569,2097,2099],{"className":2098},[731],[569,2100,2102],{"className":2101},[736],[569,2103,2105,2113],{"className":2104,"style":741},[740],[569,2106,2107,2110],{"style":744},[569,2108],{"className":2109,"style":749},[748],[569,2111,600],{"className":2112},[629,630],[569,2114,2115,2118],{"style":744},[569,2116],{"className":2117,"style":749},[748],[569,2119,2121],{"className":2120,"style":860},[761],[569,2122,2124],{"className":2123,"style":767},[766],[769,2125,2126],{"xmlns":771,"width":772,"height":773,"style":774,"viewBox":775,"preserveAspectRatio":776},[778,2127],{"d":780},[569,2129],{"className":2130,"style":636},[635],[569,2132,594],{"className":2133},[640],[569,2135],{"className":2136,"style":636},[635],[569,2138,2140,2144,2300,2303,2306],{"className":2139},[620],[569,2141],{"className":2142,"style":2143},[624],"height:3.6em;vertical-align:-1.55em;",[569,2145,2148,2196,2262],{"className":2146},[2147],"minner",[569,2149,2151],{"className":2150},[1632],[569,2152,2156],{"className":2153},[2154,2155],"delimsizing","mult",[569,2157,2159,2187],{"className":2158},[731,732],[569,2160,2162,2184],{"className":2161},[736],[569,2163,2166],{"className":2164,"style":2165},[740],"height:2.05em;",[569,2167,2169,2173],{"style":2168},"top:-4.05em;",[569,2170],{"className":2171,"style":2172},[748],"height:5.6em;",[569,2174,2176],{"style":2175},"width:0.875em;height:3.6em;",[769,2177,2181],{"xmlns":771,"width":2178,"height":2179,"viewBox":2180},"0.875em","3.6em","0 0 875 3600",[778,2182],{"d":2183},"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",[569,2185,785],{"className":2186},[784],[569,2188,2190],{"className":2189},[736],[569,2191,2194],{"className":2192,"style":2193},[740],"height:1.55em;",[569,2195],{},[569,2197,2199],{"className":2198},[629],[569,2200,2202],{"className":2201},[1975],[569,2203,2206],{"className":2204},[2205],"col-align-c",[569,2207,2209,2254],{"className":2208},[731,732],[569,2210,2212,2251],{"className":2211},[736],[569,2213,2215,2227,2239],{"className":2214,"style":2165},[740],[569,2216,2218,2221],{"style":2217},"top:-4.21em;",[569,2219],{"className":2220,"style":749},[748],[569,2222,2224],{"className":2223},[629],[569,2225,1599],{"className":2226},[629],[569,2228,2230,2233],{"style":2229},"top:-3.01em;",[569,2231],{"className":2232,"style":749},[748],[569,2234,2236],{"className":2235},[629],[569,2237,1605],{"className":2238},[629],[569,2240,2242,2245],{"style":2241},"top:-1.81em;",[569,2243],{"className":2244,"style":749},[748],[569,2246,2248],{"className":2247},[629],[569,2249,1457],{"className":2250},[629],[569,2252,785],{"className":2253},[784],[569,2255,2257],{"className":2256},[736],[569,2258,2260],{"className":2259,"style":2193},[740],[569,2261],{},[569,2263,2265],{"className":2264},[1675],[569,2266,2268],{"className":2267},[2154,2155],[569,2269,2271,2292],{"className":2270},[731,732],[569,2272,2274,2289],{"className":2273},[736],[569,2275,2277],{"className":2276,"style":2165},[740],[569,2278,2279,2282],{"style":2168},[569,2280],{"className":2281,"style":2172},[748],[569,2283,2284],{"style":2175},[769,2285,2286],{"xmlns":771,"width":2178,"height":2179,"viewBox":2180},[778,2287],{"d":2288},"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",[569,2290,785],{"className":2291},[784],[569,2293,2295],{"className":2294},[736],[569,2296,2298],{"className":2297,"style":2193},[740],[569,2299],{},[569,2301],{"className":2302,"style":660},[635],[569,2304,603],{"className":2305},[664],[569,2307],{"className":2308,"style":660},[635],[569,2310,2312,2315,2318,2321,2324],{"className":2311},[620],[569,2313],{"className":2314,"style":900},[624],[569,2316,888],{"className":2317},[629,630],[569,2319],{"className":2320,"style":660},[635],[569,2322,1362],{"className":2323},[664],[569,2325],{"className":2326,"style":660},[635],[569,2328,2330,2333],{"className":2329},[620],[569,2331],{"className":2332,"style":2143},[624],[569,2334,2336,2373,2438],{"className":2335},[2147],[569,2337,2339],{"className":2338},[1632],[569,2340,2342],{"className":2341},[2154,2155],[569,2343,2345,2365],{"className":2344},[731,732],[569,2346,2348,2362],{"className":2347},[736],[569,2349,2351],{"className":2350,"style":2165},[740],[569,2352,2353,2356],{"style":2168},[569,2354],{"className":2355,"style":2172},[748],[569,2357,2358],{"style":2175},[769,2359,2360],{"xmlns":771,"width":2178,"height":2179,"viewBox":2180},[778,2361],{"d":2183},[569,2363,785],{"className":2364},[784],[569,2366,2368],{"className":2367},[736],[569,2369,2371],{"className":2370,"style":2193},[740],[569,2372],{},[569,2374,2376],{"className":2375},[629],[569,2377,2379],{"className":2378},[1975],[569,2380,2382],{"className":2381},[2205],[569,2383,2385,2430],{"className":2384},[731,732],[569,2386,2388,2427],{"className":2387},[736],[569,2389,2391,2402,2416],{"className":2390,"style":2165},[740],[569,2392,2393,2396],{"style":2217},[569,2394],{"className":2395,"style":749},[748],[569,2397,2399],{"className":2398},[629],[569,2400,1605],{"className":2401},[629],[569,2403,2404,2407],{"style":2229},[569,2405],{"className":2406,"style":749},[748],[569,2408,2410,2413],{"className":2409},[629],[569,2411,1699],{"className":2412},[629],[569,2414,1694],{"className":2415},[629],[569,2417,2418,2421],{"style":2241},[569,2419],{"className":2420,"style":749},[748],[569,2422,2424],{"className":2423},[629],[569,2425,1706],{"className":2426},[629],[569,2428,785],{"className":2429},[784],[569,2431,2433],{"className":2432},[736],[569,2434,2436],{"className":2435,"style":2193},[740],[569,2437],{},[569,2439,2441],{"className":2440},[1675],[569,2442,2444],{"className":2443},[2154,2155],[569,2445,2447,2467],{"className":2446},[731,732],[569,2448,2450,2464],{"className":2449},[736],[569,2451,2453],{"className":2452,"style":2165},[740],[569,2454,2455,2458],{"style":2168},[569,2456],{"className":2457,"style":2172},[748],[569,2459,2460],{"style":2175},[769,2461,2462],{"xmlns":771,"width":2178,"height":2179,"viewBox":2180},[778,2463],{"d":2288},[569,2465,785],{"className":2466},[784],[569,2468,2470],{"className":2469},[736],[569,2471,2473],{"className":2472,"style":2193},[740],[569,2474],{},[565,2476,2477,2478,2529,2530,2558,2559,2610,2611,2639],{},"Für ",[569,2479,2481,2499],{"className":2480},[572],[569,2482,2484],{"className":2483},[576],[578,2485,2486],{"xmlns":580},[582,2487,2488,2496],{},[585,2489,2490,2492,2494],{},[588,2491,888],{},[592,2493,594],{},[1455,2495,1457],{},[608,2497,2498],{"encoding":610},"t = 0",[569,2500,2502,2520],{"className":2501,"ariaHidden":616},[615],[569,2503,2505,2508,2511,2514,2517],{"className":2504},[620],[569,2506],{"className":2507,"style":900},[624],[569,2509,888],{"className":2510},[629,630],[569,2512],{"className":2513,"style":636},[635],[569,2515,594],{"className":2516},[640],[569,2518],{"className":2519,"style":636},[635],[569,2521,2523,2526],{"className":2522},[620],[569,2524],{"className":2525,"style":1529},[624],[569,2527,1457],{"className":2528},[629]," erhält man ",[569,2531,2533,2546],{"className":2532},[572],[569,2534,2536],{"className":2535},[576],[578,2537,2538],{"xmlns":580},[582,2539,2540,2544],{},[585,2541,2542],{},[588,2543,1019],{},[608,2545,1019],{"encoding":610},[569,2547,2549],{"className":2548,"ariaHidden":616},[615],[569,2550,2552,2555],{"className":2551},[620],[569,2553],{"className":2554,"style":931},[624],[569,2556,1019],{"className":2557},[629,630],", für ",[569,2560,2562,2580],{"className":2561},[572],[569,2563,2565],{"className":2564},[576],[578,2566,2567],{"xmlns":580},[582,2568,2569,2577],{},[585,2570,2571,2573,2575],{},[588,2572,888],{},[592,2574,594],{},[1455,2576,1599],{},[608,2578,2579],{"encoding":610},"t = 1",[569,2581,2583,2601],{"className":2582,"ariaHidden":616},[615],[569,2584,2586,2589,2592,2595,2598],{"className":2585},[620],[569,2587],{"className":2588,"style":900},[624],[569,2590,888],{"className":2591},[629,630],[569,2593],{"className":2594,"style":636},[635],[569,2596,594],{"className":2597},[640],[569,2599],{"className":2600,"style":636},[635],[569,2602,2604,2607],{"className":2603},[620],[569,2605],{"className":2606,"style":1529},[624],[569,2608,1599],{"className":2609},[629]," den Punkt ",[569,2612,2614,2627],{"className":2613},[572],[569,2615,2617],{"className":2616},[576],[578,2618,2619],{"xmlns":580},[582,2620,2621,2625],{},[585,2622,2623],{},[588,2624,1049],{},[608,2626,1049],{"encoding":610},[569,2628,2630],{"className":2629,"ariaHidden":616},[615],[569,2631,2633,2636],{"className":2632},[620],[569,2634],{"className":2635,"style":931},[624],[569,2637,1049],{"className":2638,"style":1064},[629,630],".",[565,2641,2642,2643,2738,2739,2767,2768,2847,2848,2899,2900,1034,3000,3095,3096,3124,3125,2639],{},"Liegt ",[569,2644,2646,2678],{"className":2645},[572],[569,2647,2649],{"className":2648},[576],[578,2650,2651],{"xmlns":580},[582,2652,2653,2675],{},[585,2654,2655,2657,2659,2662,2664,2666,2668,2670,2673],{},[588,2656,919],{},[592,2658,1596],{"stretchy":1595},[1455,2660,2661],{},"7",[592,2663,1602],{},[592,2665,1699],{},[1455,2667,2661],{},[592,2669,1602],{},[1455,2671,2672],{},"12",[592,2674,1612],{"stretchy":1595},[608,2676,2677],{"encoding":610},"P(7 \\mid -7 \\mid 12)",[569,2679,2681,2705,2726],{"className":2680,"ariaHidden":616},[615],[569,2682,2684,2687,2690,2693,2696,2699,2702],{"className":2683},[620],[569,2685],{"className":2686,"style":1625},[624],[569,2688,919],{"className":2689,"style":935},[629,630],[569,2691,1596],{"className":2692},[1632],[569,2694,2661],{"className":2695},[629],[569,2697],{"className":2698,"style":636},[635],[569,2700,1602],{"className":2701},[640],[569,2703],{"className":2704,"style":636},[635],[569,2706,2708,2711,2714,2717,2720,2723],{"className":2707},[620],[569,2709],{"className":2710,"style":1625},[624],[569,2712,1699],{"className":2713},[629],[569,2715,2661],{"className":2716},[629],[569,2718],{"className":2719,"style":636},[635],[569,2721,1602],{"className":2722},[640],[569,2724],{"className":2725,"style":636},[635],[569,2727,2729,2732,2735],{"className":2728},[620],[569,2730],{"className":2731,"style":1625},[624],[569,2733,2672],{"className":2734},[629],[569,2736,1612],{"className":2737},[1675]," auf ",[569,2740,2742,2755],{"className":2741},[572],[569,2743,2745],{"className":2744},[576],[578,2746,2747],{"xmlns":580},[582,2748,2749,2753],{},[585,2750,2751],{},[588,2752,1944],{},[608,2754,1944],{"encoding":610},[569,2756,2758],{"className":2757,"ariaHidden":616},[615],[569,2759,2761,2764],{"className":2760},[620],[569,2762],{"className":2763,"style":625},[624],[569,2765,1944],{"className":2766,"style":631},[629,630],"? Aus der ersten Zeile ",[569,2769,2771,2795],{"className":2770},[572],[569,2772,2774],{"className":2773},[576],[578,2775,2776],{"xmlns":580},[582,2777,2778,2792],{},[585,2779,2780,2782,2784,2786,2788,2790],{},[1455,2781,1599],{},[592,2783,603],{},[1455,2785,1605],{},[588,2787,888],{},[592,2789,594],{},[1455,2791,2661],{},[608,2793,2794],{"encoding":610},"1 + 2t = 7",[569,2796,2798,2817,2838],{"className":2797,"ariaHidden":616},[615],[569,2799,2801,2805,2808,2811,2814],{"className":2800},[620],[569,2802],{"className":2803,"style":2804},[624],"height:0.7278em;vertical-align:-0.0833em;",[569,2806,1599],{"className":2807},[629],[569,2809],{"className":2810,"style":660},[635],[569,2812,603],{"className":2813},[664],[569,2815],{"className":2816,"style":660},[635],[569,2818,2820,2823,2826,2829,2832,2835],{"className":2819},[620],[569,2821],{"className":2822,"style":1529},[624],[569,2824,1605],{"className":2825},[629],[569,2827,888],{"className":2828},[629,630],[569,2830],{"className":2831,"style":636},[635],[569,2833,594],{"className":2834},[640],[569,2836],{"className":2837,"style":636},[635],[569,2839,2841,2844],{"className":2840},[620],[569,2842],{"className":2843,"style":1529},[624],[569,2845,2661],{"className":2846},[629]," folgt ",[569,2849,2851,2869],{"className":2850},[572],[569,2852,2854],{"className":2853},[576],[578,2855,2856],{"xmlns":580},[582,2857,2858,2866],{},[585,2859,2860,2862,2864],{},[588,2861,888],{},[592,2863,594],{},[1455,2865,1694],{},[608,2867,2868],{"encoding":610},"t = 3",[569,2870,2872,2890],{"className":2871,"ariaHidden":616},[615],[569,2873,2875,2878,2881,2884,2887],{"className":2874},[620],[569,2876],{"className":2877,"style":900},[624],[569,2879,888],{"className":2880},[629,630],[569,2882],{"className":2883,"style":636},[635],[569,2885,594],{"className":2886},[640],[569,2888],{"className":2889,"style":636},[635],[569,2891,2893,2896],{"className":2892},[620],[569,2894],{"className":2895,"style":1529},[624],[569,2897,1694],{"className":2898},[629],". Probe: ",[569,2901,2903,2931],{"className":2902},[572],[569,2904,2906],{"className":2905},[576],[578,2907,2908],{"xmlns":580},[582,2909,2910,2928],{},[585,2911,2912,2914,2916,2918,2920,2922,2924,2926],{},[1455,2913,1605],{},[592,2915,1699],{},[1455,2917,1694],{},[592,2919,1362],{},[1455,2921,1694],{},[592,2923,594],{},[592,2925,1699],{},[1455,2927,2661],{},[608,2929,2930],{"encoding":610},"2 - 3 \\cdot 3 = -7",[569,2932,2934,2952,2970,2988],{"className":2933,"ariaHidden":616},[615],[569,2935,2937,2940,2943,2946,2949],{"className":2936},[620],[569,2938],{"className":2939,"style":2804},[624],[569,2941,1605],{"className":2942},[629],[569,2944],{"className":2945,"style":660},[635],[569,2947,1699],{"className":2948},[664],[569,2950],{"className":2951,"style":660},[635],[569,2953,2955,2958,2961,2964,2967],{"className":2954},[620],[569,2956],{"className":2957,"style":1529},[624],[569,2959,1694],{"className":2960},[629],[569,2962],{"className":2963,"style":660},[635],[569,2965,1362],{"className":2966},[664],[569,2968],{"className":2969,"style":660},[635],[569,2971,2973,2976,2979,2982,2985],{"className":2972},[620],[569,2974],{"className":2975,"style":1529},[624],[569,2977,1694],{"className":2978},[629],[569,2980],{"className":2981,"style":636},[635],[569,2983,594],{"className":2984},[640],[569,2986],{"className":2987,"style":636},[635],[569,2989,2991,2994,2997],{"className":2990},[620],[569,2992],{"className":2993,"style":2804},[624],[569,2995,1699],{"className":2996},[629],[569,2998,2661],{"className":2999},[629],[569,3001,3003,3029],{"className":3002},[572],[569,3004,3006],{"className":3005},[576],[578,3007,3008],{"xmlns":580},[582,3009,3010,3026],{},[585,3011,3012,3014,3016,3018,3020,3022,3024],{},[1455,3013,1457],{},[592,3015,603],{},[1455,3017,1706],{},[592,3019,1362],{},[1455,3021,1694],{},[592,3023,594],{},[1455,3025,2672],{},[608,3027,3028],{"encoding":610},"0 + 4 \\cdot 3 = 12",[569,3030,3032,3050,3068,3086],{"className":3031,"ariaHidden":616},[615],[569,3033,3035,3038,3041,3044,3047],{"className":3034},[620],[569,3036],{"className":3037,"style":2804},[624],[569,3039,1457],{"className":3040},[629],[569,3042],{"className":3043,"style":660},[635],[569,3045,603],{"className":3046},[664],[569,3048],{"className":3049,"style":660},[635],[569,3051,3053,3056,3059,3062,3065],{"className":3052},[620],[569,3054],{"className":3055,"style":1529},[624],[569,3057,1706],{"className":3058},[629],[569,3060],{"className":3061,"style":660},[635],[569,3063,1362],{"className":3064},[664],[569,3066],{"className":3067,"style":660},[635],[569,3069,3071,3074,3077,3080,3083],{"className":3070},[620],[569,3072],{"className":3073,"style":1529},[624],[569,3075,1694],{"className":3076},[629],[569,3078],{"className":3079,"style":636},[635],[569,3081,594],{"className":3082},[640],[569,3084],{"className":3085,"style":636},[635],[569,3087,3089,3092],{"className":3088},[620],[569,3090],{"className":3091,"style":1529},[624],[569,3093,2672],{"className":3094},[629],". Alle Zeilen passen, ",[569,3097,3099,3112],{"className":3098},[572],[569,3100,3102],{"className":3101},[576],[578,3103,3104],{"xmlns":580},[582,3105,3106,3110],{},[585,3107,3108],{},[588,3109,919],{},[608,3111,919],{"encoding":610},[569,3113,3115],{"className":3114,"ariaHidden":616},[615],[569,3116,3118,3121],{"className":3117},[620],[569,3119],{"className":3120,"style":931},[624],[569,3122,919],{"className":3123,"style":935},[629,630]," liegt auf ",[569,3126,3128,3141],{"className":3127},[572],[569,3129,3131],{"className":3130},[576],[578,3132,3133],{"xmlns":580},[582,3134,3135,3139],{},[585,3136,3137],{},[588,3138,1944],{},[608,3140,1944],{"encoding":610},[569,3142,3144],{"className":3143,"ariaHidden":616},[615],[569,3145,3147,3150],{"className":3146},[620],[569,3148],{"className":3149,"style":625},[624],[569,3151,1944],{"className":3152,"style":631},[629,630],[565,3154,2642,3155,2738,3251,3279,3280,2847,3358,3409,3410,3489,3490,3641,3642,3671,3672,2639],{},[569,3156,3158,3191],{"className":3157},[572],[569,3159,3161],{"className":3160},[576],[578,3162,3163],{"xmlns":580},[582,3164,3165,3188],{},[585,3166,3167,3170,3172,3175,3177,3179,3181,3183,3186],{},[588,3168,3169],{},"Q",[592,3171,1596],{"stretchy":1595},[1455,3173,3174],{},"5",[592,3176,1602],{},[592,3178,1699],{},[1455,3180,1706],{},[592,3182,1602],{},[1455,3184,3185],{},"9",[592,3187,1612],{"stretchy":1595},[608,3189,3190],{"encoding":610},"Q(5 \\mid -4 \\mid 9)",[569,3192,3194,3218,3239],{"className":3193,"ariaHidden":616},[615],[569,3195,3197,3200,3203,3206,3209,3212,3215],{"className":3196},[620],[569,3198],{"className":3199,"style":1625},[624],[569,3201,3169],{"className":3202},[629,630],[569,3204,1596],{"className":3205},[1632],[569,3207,3174],{"className":3208},[629],[569,3210],{"className":3211,"style":636},[635],[569,3213,1602],{"className":3214},[640],[569,3216],{"className":3217,"style":636},[635],[569,3219,3221,3224,3227,3230,3233,3236],{"className":3220},[620],[569,3222],{"className":3223,"style":1625},[624],[569,3225,1699],{"className":3226},[629],[569,3228,1706],{"className":3229},[629],[569,3231],{"className":3232,"style":636},[635],[569,3234,1602],{"className":3235},[640],[569,3237],{"className":3238,"style":636},[635],[569,3240,3242,3245,3248],{"className":3241},[620],[569,3243],{"className":3244,"style":1625},[624],[569,3246,3185],{"className":3247},[629],[569,3249,1612],{"className":3250},[1675],[569,3252,3254,3267],{"className":3253},[572],[569,3255,3257],{"className":3256},[576],[578,3258,3259],{"xmlns":580},[582,3260,3261,3265],{},[585,3262,3263],{},[588,3264,1944],{},[608,3266,1944],{"encoding":610},[569,3268,3270],{"className":3269,"ariaHidden":616},[615],[569,3271,3273,3276],{"className":3272},[620],[569,3274],{"className":3275,"style":625},[624],[569,3277,1944],{"className":3278,"style":631},[629,630],"? Aus ",[569,3281,3283,3307],{"className":3282},[572],[569,3284,3286],{"className":3285},[576],[578,3287,3288],{"xmlns":580},[582,3289,3290,3304],{},[585,3291,3292,3294,3296,3298,3300,3302],{},[1455,3293,1599],{},[592,3295,603],{},[1455,3297,1605],{},[588,3299,888],{},[592,3301,594],{},[1455,3303,3174],{},[608,3305,3306],{"encoding":610},"1 + 2t = 5",[569,3308,3310,3328,3349],{"className":3309,"ariaHidden":616},[615],[569,3311,3313,3316,3319,3322,3325],{"className":3312},[620],[569,3314],{"className":3315,"style":2804},[624],[569,3317,1599],{"className":3318},[629],[569,3320],{"className":3321,"style":660},[635],[569,3323,603],{"className":3324},[664],[569,3326],{"className":3327,"style":660},[635],[569,3329,3331,3334,3337,3340,3343,3346],{"className":3330},[620],[569,3332],{"className":3333,"style":1529},[624],[569,3335,1605],{"className":3336},[629],[569,3338,888],{"className":3339},[629,630],[569,3341],{"className":3342,"style":636},[635],[569,3344,594],{"className":3345},[640],[569,3347],{"className":3348,"style":636},[635],[569,3350,3352,3355],{"className":3351},[620],[569,3353],{"className":3354,"style":1529},[624],[569,3356,3174],{"className":3357},[629],[569,3359,3361,3379],{"className":3360},[572],[569,3362,3364],{"className":3363},[576],[578,3365,3366],{"xmlns":580},[582,3367,3368,3376],{},[585,3369,3370,3372,3374],{},[588,3371,888],{},[592,3373,594],{},[1455,3375,1605],{},[608,3377,3378],{"encoding":610},"t = 2",[569,3380,3382,3400],{"className":3381,"ariaHidden":616},[615],[569,3383,3385,3388,3391,3394,3397],{"className":3384},[620],[569,3386],{"className":3387,"style":900},[624],[569,3389,888],{"className":3390},[629,630],[569,3392],{"className":3393,"style":636},[635],[569,3395,594],{"className":3396},[640],[569,3398],{"className":3399,"style":636},[635],[569,3401,3403,3406],{"className":3402},[620],[569,3404],{"className":3405,"style":1529},[624],[569,3407,1605],{"className":3408},[629],", die zweite Zeile passt mit ",[569,3411,3413,3438],{"className":3412},[572],[569,3414,3416],{"className":3415},[576],[578,3417,3418],{"xmlns":580},[582,3419,3420,3435],{},[585,3421,3422,3424,3426,3429,3431,3433],{},[1455,3423,1605],{},[592,3425,1699],{},[1455,3427,3428],{},"6",[592,3430,594],{},[592,3432,1699],{},[1455,3434,1706],{},[608,3436,3437],{"encoding":610},"2 - 6 = -4",[569,3439,3441,3459,3477],{"className":3440,"ariaHidden":616},[615],[569,3442,3444,3447,3450,3453,3456],{"className":3443},[620],[569,3445],{"className":3446,"style":2804},[624],[569,3448,1605],{"className":3449},[629],[569,3451],{"className":3452,"style":660},[635],[569,3454,1699],{"className":3455},[664],[569,3457],{"className":3458,"style":660},[635],[569,3460,3462,3465,3468,3471,3474],{"className":3461},[620],[569,3463],{"className":3464,"style":1529},[624],[569,3466,3428],{"className":3467},[629],[569,3469],{"className":3470,"style":636},[635],[569,3472,594],{"className":3473},[640],[569,3475],{"className":3476,"style":636},[635],[569,3478,3480,3483,3486],{"className":3479},[620],[569,3481],{"className":3482,"style":2804},[624],[569,3484,1699],{"className":3485},[629],[569,3487,1706],{"className":3488},[629],". Die dritte Zeile liefert aber ",[569,3491,3493,3524],{"className":3492},[572],[569,3494,3496],{"className":3495},[576],[578,3497,3498],{"xmlns":580},[582,3499,3500,3521],{},[585,3501,3502,3504,3506,3508,3510,3512,3514,3517,3519],{},[1455,3503,1457],{},[592,3505,603],{},[1455,3507,1706],{},[592,3509,1362],{},[1455,3511,1605],{},[592,3513,594],{},[1455,3515,3516],{},"8",[592,3518,1453],{"mathvariant":1452},[1455,3520,3185],{},[608,3522,3523],{"encoding":610},"0 + 4 \\cdot 2 = 8 \\neq 9",[569,3525,3527,3545,3563,3581,3632],{"className":3526,"ariaHidden":616},[615],[569,3528,3530,3533,3536,3539,3542],{"className":3529},[620],[569,3531],{"className":3532,"style":2804},[624],[569,3534,1457],{"className":3535},[629],[569,3537],{"className":3538,"style":660},[635],[569,3540,603],{"className":3541},[664],[569,3543],{"className":3544,"style":660},[635],[569,3546,3548,3551,3554,3557,3560],{"className":3547},[620],[569,3549],{"className":3550,"style":1529},[624],[569,3552,1706],{"className":3553},[629],[569,3555],{"className":3556,"style":660},[635],[569,3558,1362],{"className":3559},[664],[569,3561],{"className":3562,"style":660},[635],[569,3564,3566,3569,3572,3575,3578],{"className":3565},[620],[569,3567],{"className":3568,"style":1529},[624],[569,3570,1605],{"className":3571},[629],[569,3573],{"className":3574,"style":636},[635],[569,3576,594],{"className":3577},[640],[569,3579],{"className":3580,"style":636},[635],[569,3582,3584,3587,3590,3593,3629],{"className":3583},[620],[569,3585],{"className":3586,"style":1470},[624],[569,3588,3516],{"className":3589},[629],[569,3591],{"className":3592,"style":636},[635],[569,3594,3596,3623,3626],{"className":3595},[640],[569,3597,3599],{"className":3598},[640],[569,3600,3602],{"className":3601},[629,1486],[569,3603,3605],{"className":3604},[1490],[569,3606,3608,3611,3620],{"className":3607},[1494],[569,3609],{"className":3610,"style":1470},[624],[569,3612,3614],{"className":3613},[1501],[569,3615,3617],{"className":3616},[629],[569,3618,1508],{"className":3619},[640],[569,3621],{"className":3622},[1512],[569,3624],{"className":3625},[635,1516],[569,3627,594],{"className":3628},[640],[569,3630],{"className":3631,"style":636},[635],[569,3633,3635,3638],{"className":3634},[620],[569,3636],{"className":3637,"style":1529},[624],[569,3639,3185],{"className":3640},[629],". ",[569,3643,3645,3658],{"className":3644},[572],[569,3646,3648],{"className":3647},[576],[578,3649,3650],{"xmlns":580},[582,3651,3652,3656],{},[585,3653,3654],{},[588,3655,3169],{},[608,3657,3169],{"encoding":610},[569,3659,3661],{"className":3660,"ariaHidden":616},[615],[569,3662,3664,3668],{"className":3663},[620],[569,3665],{"className":3666,"style":3667},[624],"height:0.8778em;vertical-align:-0.1944em;",[569,3669,3169],{"className":3670},[629,630]," liegt nicht auf ",[569,3673,3675,3688],{"className":3674},[572],[569,3676,3678],{"className":3677},[576],[578,3679,3680],{"xmlns":580},[582,3681,3682,3686],{},[585,3683,3684],{},[588,3685,1944],{},[608,3687,1944],{"encoding":610},[569,3689,3691],{"className":3690,"ariaHidden":616},[615],[569,3692,3694,3697],{"className":3693},[620],[569,3695],{"className":3696,"style":625},[624],[569,3698,1944],{"className":3699,"style":631},[629,630],[560,3701,3703],{"id":3702},"typische-fehler","Typische Fehler",[680,3705,3706,3930,3962],{},[683,3707,3708,3709,3737,3738,2639],{},"Den Ortsvektor von ",[569,3710,3712,3725],{"className":3711},[572],[569,3713,3715],{"className":3714},[576],[578,3716,3717],{"xmlns":580},[582,3718,3719,3723],{},[585,3720,3721],{},[588,3722,1049],{},[608,3724,1049],{"encoding":610},[569,3726,3728],{"className":3727,"ariaHidden":616},[615],[569,3729,3731,3734],{"className":3730},[620],[569,3732],{"className":3733,"style":931},[624],[569,3735,1049],{"className":3736,"style":1064},[629,630]," als Richtungsvektor nehmen. Der Richtungsvektor ist ",[569,3739,3741,3779],{"className":3740},[572],[569,3742,3744],{"className":3743},[576],[578,3745,3746],{"xmlns":580},[582,3747,3748,3776],{},[585,3749,3750,3760,3762,3768,3770],{},[704,3751,3752,3758],{"accent":616},[585,3753,3754,3756],{},[588,3755,1019],{},[588,3757,1049],{},[592,3759,1232],{"stretchy":616},[592,3761,594],{},[704,3763,3764,3766],{"accent":616},[588,3765,606],{},[592,3767,710],{},[592,3769,1699],{},[704,3771,3772,3774],{"accent":616},[588,3773,1090],{},[592,3775,710],{},[608,3777,3778],{"encoding":610},"\\overrightarrow{AB} = \\vec{b} - \\vec{a}",[569,3780,3782,3836,3889],{"className":3781,"ariaHidden":616},[615],[569,3783,3785,3788,3827,3830,3833],{"className":3784},[620],[569,3786],{"className":3787,"style":1295},[624],[569,3789,3791],{"className":3790},[629,727],[569,3792,3794],{"className":3793},[731],[569,3795,3797],{"className":3796},[736],[569,3798,3800,3814],{"className":3799,"style":1295},[740],[569,3801,3802,3805],{"style":744},[569,3803],{"className":3804,"style":749},[748],[569,3806,3808,3811],{"className":3807},[629],[569,3809,1019],{"className":3810},[629,630],[569,3812,1049],{"className":3813,"style":1064},[629,630],[569,3815,3817,3820],{"className":3816,"style":1326},[1325],[569,3818],{"className":3819,"style":749},[748],[569,3821,3823],{"className":3822,"style":1334},[1333],[769,3824,3825],{"xmlns":771,"width":1337,"height":1338,"viewBox":1339,"preserveAspectRatio":1340},[778,3826],{"d":1343},[569,3828],{"className":3829,"style":636},[635],[569,3831,594],{"className":3832},[640],[569,3834],{"className":3835,"style":636},[635],[569,3837,3839,3843,3880,3883,3886],{"className":3838},[620],[569,3840],{"className":3841,"style":3842},[624],"height:1.0608em;vertical-align:-0.0833em;",[569,3844,3846],{"className":3845},[629,727],[569,3847,3849],{"className":3848},[731],[569,3850,3852],{"className":3851},[736],[569,3853,3856,3864],{"className":3854,"style":3855},[740],"height:0.9774em;",[569,3857,3858,3861],{"style":744},[569,3859],{"className":3860,"style":749},[748],[569,3862,606],{"className":3863},[629,630],[569,3865,3867,3870],{"style":3866},"top:-3.2634em;",[569,3868],{"className":3869,"style":749},[748],[569,3871,3873],{"className":3872,"style":1194},[761],[569,3874,3876],{"className":3875,"style":767},[766],[769,3877,3878],{"xmlns":771,"width":772,"height":773,"style":774,"viewBox":775,"preserveAspectRatio":776},[778,3879],{"d":780},[569,3881],{"className":3882,"style":660},[635],[569,3884,1699],{"className":3885},[664],[569,3887],{"className":3888,"style":660},[635],[569,3890,3892,3895],{"className":3891},[620],[569,3893],{"className":3894,"style":741},[624],[569,3896,3898],{"className":3897},[629,727],[569,3899,3901],{"className":3900},[731],[569,3902,3904],{"className":3903},[736],[569,3905,3907,3915],{"className":3906,"style":741},[740],[569,3908,3909,3912],{"style":744},[569,3910],{"className":3911,"style":749},[748],[569,3913,1090],{"className":3914},[629,630],[569,3916,3917,3920],{"style":744},[569,3918],{"className":3919,"style":749},[748],[569,3921,3923],{"className":3922,"style":1194},[761],[569,3924,3926],{"className":3925,"style":767},[766],[769,3927,3928],{"xmlns":771,"width":772,"height":773,"style":774,"viewBox":775,"preserveAspectRatio":776},[778,3929],{"d":780},[683,3931,3932,3933,3961],{},"Bei der Punktprobe in jeder Zeile ein anderes ",[569,3934,3936,3949],{"className":3935},[572],[569,3937,3939],{"className":3938},[576],[578,3940,3941],{"xmlns":580},[582,3942,3943,3947],{},[585,3944,3945],{},[588,3946,888],{},[608,3948,888],{"encoding":610},[569,3950,3952],{"className":3951,"ariaHidden":616},[615],[569,3953,3955,3958],{"className":3954},[620],[569,3956],{"className":3957,"style":900},[624],[569,3959,888],{"className":3960},[629,630]," zulassen. Der Parameter muss in allen drei Zeilen gleich sein.",[683,3963,3964],{},"Nach zwei passenden Zeilen aufhören. Erst wenn auch die dritte Zeile stimmt, liegt der Punkt auf der Geraden.",{"title":3966,"searchDepth":3967,"depth":3967,"links":3968},"",2,[3969,3970,3971],{"id":562,"depth":3967,"text":563},{"id":1574,"depth":3967,"text":1575},{"id":3702,"depth":3967,"text":3703},[3973,3975,3978,3980,3984,3987,3991,3994,3996,3999],{"lhs":3974,"rhs":1605},"3 - 1",{"lhs":3976,"rhs":3977},"-1 - 2","-3",{"lhs":3979,"rhs":1706},"4 - 0",{"lhs":3981,"rhs":1694,"where":3982},"1 + t*2",{"t":3983},1,{"lhs":3981,"rhs":2661,"where":3985},{"t":3986},3,{"lhs":3988,"rhs":3989,"where":3990},"2 + t*(-3)","-7",{"t":3986},{"lhs":3992,"rhs":2672,"where":3993},"0 + t*4",{"t":3986},{"lhs":3981,"rhs":3174,"where":3995},{"t":3967},{"lhs":3988,"rhs":3997,"where":3998},"-4",{"t":3967},{"lhs":3992,"rhs":3516,"where":4000},{"t":3967},"\\vec{u} \\neq \\vec{0},\\ t \\in \\mathbb{R}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmn>0\u003C\u002Fmn>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{u} \\neq \\vec{0},\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:0.9084em;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\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\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\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1219em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.9274em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2134em;\">\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>t\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">t \\in \\mathbb{R}\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:0.6542em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","line-parametric-form","g\\colon \\vec{x} = \\vec{p} + t \\cdot \\vec{u}","\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>g\u003C\u002Fmi>\u003Cmspace>\u003C\u002Fmspace>\u003Cmspace width=\"0.1111em\"\u002F>\u003Cmo lspace=\"0em\" rspace=\"0.17em\">\u003C\u002Fmo>\u003Cmtext> ⁣\u003C\u002Fmtext>\u003Cmo lspace=\"0em\" rspace=\"0em\">:\u003C\u002Fmo>\u003Cmspace width=\"0.3333em\"\u002F>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>p\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">g\\colon \\vec{x} = \\vec{p} + t \\cdot \\vec{u}\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:0.9084em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">g\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1111em;\">\u003C\u002Fspan>\u003Cspan class=\"mpunct\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:-0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">:\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.3333em;\">\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\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\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:0.9084em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t vlist-t2\">\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\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1522em;\">\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>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1944em;\">\u003Cspan>\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>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6151em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\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>\u003C\u002Fspan>\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\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\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>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fparameterform-gerade",[],[4014,4015,4016,4017],"vector-between-points","plane-parametric-form","distance-point-line","angle-line-plane",{"title":548,"description":3966},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fparameterform-gerade","Jeder Punkt einer Geraden entsteht aus einem festen Punkt plus einem Vielfachen des Richtungsvektors.",[4022,4023,4024,4025,4026],"gerade","parameterform","richtungsvektor","stützvektor","analytische geometrie",[4028,4031,4035,4038,4041],{"symbol":1944,"meaning":4029,"symbolHtml":4030},"Name der Geraden","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>g\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">g\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 mathnormal\" style=\"margin-right:0.0359em;\">g\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4032,"meaning":4033,"symbolHtml":4034},"\\vec{x}","Ortsvektor eines beliebigen Punkts der Geraden","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{x}\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\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\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":713,"meaning":4036,"symbolHtml":4037},"Stützvektor, Ortsvektor eines festen Punkts P der Geraden","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>p\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{p}\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:0.9084em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t vlist-t2\">\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\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1522em;\">\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>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1944em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":822,"meaning":4039,"symbolHtml":4040},"Richtungsvektor, gibt die Richtung der Geraden an","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{u}\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\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\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":888,"meaning":4042,"symbolHtml":4043},"Parameter, eine reelle Zahl; jeder Wert liefert einen Punkt der Geraden","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>t\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">t\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:0.6151em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","9eSM-5V8ny3YnCTQFcHlV5hvGqAiOBvMsNovVkFOd00",[4046,4049,4052,4055],{"stem":4047,"title":4048,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fabstand-punkt-gerade","Abstand Punkt–Gerade im Raum",{"stem":4050,"title":4051,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fparameterform-ebene","Parameterform einer Ebene",{"stem":4053,"title":4054,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fschnittwinkel-gerade-ebene","Schnittwinkel Gerade–Ebene",{"stem":4056,"title":4057,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fverbindungsvektor","Verbindungsvektor",1793824279593]