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",[567,1082,1084,1114],{"className":1083},[570],[567,1085,1087],{"className":1086},[574],[576,1088,1089],{"xmlns":578},[580,1090,1091,1111],{},[583,1092,1093,1095,1101,1103,1105,1107,1109],{},[590,1094,767],{"mathvariant":766},[586,1096,1097,1099],{"accent":588},[590,1098,689],{},[594,1100,596],{},[590,1102,767],{"mathvariant":766},[594,1104,800],{},[590,1106,815],{},[594,1108,818],{},[590,1110,821],{},[598,1112,1113],{"encoding":600},"|\\vec{b}| \\cdot \\sin\\varphi",[567,1115,1117,1173],{"className":1116,"ariaHidden":588},[605],[567,1118,1120,1123,1126,1161,1164,1167,1170],{"className":1119},[609],[567,1121],{"className":1122,"style":894},[613],[567,1124,767],{"className":1125},[618],[567,1127,1129],{"className":1128},[618,619],[567,1130,1132],{"className":1131},[623],[567,1133,1135],{"className":1134},[627],[567,1136,1138,1146],{"className":1137,"style":704},[631],[567,1139,1140,1143],{"style":634},[567,1141],{"className":1142,"style":639},[638],[567,1144,689],{"className":1145},[618,643],[567,1147,1148,1151],{"style":727},[567,1149],{"className":1150,"style":639},[638],[567,1152,1154],{"className":1153,"style":653},[652],[567,1155,1157],{"className":1156,"style":658},[657],[660,1158,1159],{"xmlns":662,"width":663,"height":664,"style":665,"viewBox":666,"preserveAspectRatio":667},[669,1160],{"d":671},[567,1162,767],{"className":1163},[618],[567,1165],{"className":1166,"style":880},[879],[567,1168,800],{"className":1169},[884],[567,1171],{"className":1172,"style":880},[879],[567,1174,1176,1179,1182,1185],{"className":1175},[609],[567,1177],{"className":1178,"style":1062},[613],[567,1180,815],{"className":1181},[1066],[567,1183],{"className":1184,"style":1070},[879],[567,1186,821],{"className":1187},[618,643]," ist genau die Höhe auf der Seite ",[567,1190,1192,1209],{"className":1191},[570],[567,1193,1195],{"className":1194},[574],[576,1196,1197],{"xmlns":578},[580,1198,1199,1207],{},[583,1200,1201],{},[586,1202,1203,1205],{"accent":588},[590,1204,592],{},[594,1206,596],{},[598,1208,601],{"encoding":600},[567,1210,1212],{"className":1211,"ariaHidden":588},[605],[567,1213,1215,1218],{"className":1214},[609],[567,1216],{"className":1217,"style":614},[613],[567,1219,1221],{"className":1220},[618,619],[567,1222,1224],{"className":1223},[623],[567,1225,1227],{"className":1226},[627],[567,1228,1230,1238],{"className":1229,"style":614},[631],[567,1231,1232,1235],{"style":634},[567,1233],{"className":1234,"style":639},[638],[567,1236,592],{"className":1237},[618,643],[567,1239,1240,1243],{"style":634},[567,1241],{"className":1242,"style":639},[638],[567,1244,1246],{"className":1245,"style":653},[652],[567,1247,1249],{"className":1248,"style":658},[657],[660,1250,1251],{"xmlns":662,"width":663,"height":664,"style":665,"viewBox":666,"preserveAspectRatio":667},[669,1252],{"d":671},".",[563,1255,1256,1257,1309,1310,672,1452,1583],{},"Bei einem Parallelogramm ",[567,1258,1260,1284],{"className":1259},[570],[567,1261,1263],{"className":1262},[574],[576,1264,1265],{"xmlns":578},[580,1266,1267,1281],{},[583,1268,1269,1272,1275,1278],{},[590,1270,1271],{},"A",[590,1273,1274],{},"B",[590,1276,1277],{},"C",[590,1279,1280],{},"D",[598,1282,1283],{"encoding":600},"ABCD",[567,1285,1287],{"className":1286,"ariaHidden":588},[605],[567,1288,1290,1294,1297,1301,1305],{"className":1289},[609],[567,1291],{"className":1292,"style":1293},[613],"height:0.6833em;",[567,1295,1271],{"className":1296},[618,643],[567,1298,1274],{"className":1299,"style":1300},[618,643],"margin-right:0.0502em;",[567,1302,1277],{"className":1303,"style":1304},[618,643],"margin-right:0.0715em;",[567,1306,1280],{"className":1307,"style":1308},[618,643],"margin-right:0.0278em;"," nimmt man ",[567,1311,1313,1344],{"className":1312},[570],[567,1314,1316],{"className":1315},[574],[576,1317,1318],{"xmlns":578},[580,1319,1320,1341],{},[583,1321,1322,1328,1330],{},[586,1323,1324,1326],{"accent":588},[590,1325,592],{},[594,1327,596],{},[594,1329,787],{},[586,1331,1332,1338],{"accent":588},[583,1333,1334,1336],{},[590,1335,1271],{},[590,1337,1274],{},[594,1339,1340],{"stretchy":588},"→",[598,1342,1343],{"encoding":600},"\\vec{a} = \\overrightarrow{AB}",[567,1345,1347,1397],{"className":1346,"ariaHidden":588},[605],[567,1348,1350,1353,1388,1391,1394],{"className":1349},[609],[567,1351],{"className":1352,"style":614},[613],[567,1354,1356],{"className":1355},[618,619],[567,1357,1359],{"className":1358},[623],[567,1360,1362],{"className":1361},[627],[567,1363,1365,1373],{"className":1364,"style":614},[631],[567,1366,1367,1370],{"style":634},[567,1368],{"className":1369,"style":639},[638],[567,1371,592],{"className":1372},[618,643],[567,1374,1375,1378],{"style":634},[567,1376],{"className":1377,"style":639},[638],[567,1379,1381],{"className":1380,"style":653},[652],[567,1382,1384],{"className":1383,"style":658},[657],[660,1385,1386],{"xmlns":662,"width":663,"height":664,"style":665,"viewBox":666,"preserveAspectRatio":667},[669,1387],{"d":671},[567,1389],{"className":1390,"style":936},[879],[567,1392,787],{"className":1393},[940],[567,1395],{"className":1396,"style":936},[879],[567,1398,1400,1404],{"className":1399},[609],[567,1401],{"className":1402,"style":1403},[613],"height:1.2053em;",[567,1405,1407],{"className":1406},[618,619],[567,1408,1410],{"className":1409},[623],[567,1411,1413],{"className":1412},[627],[567,1414,1416,1430],{"className":1415,"style":1403},[631],[567,1417,1418,1421],{"style":634},[567,1419],{"className":1420,"style":639},[638],[567,1422,1424,1427],{"className":1423},[618],[567,1425,1271],{"className":1426},[618,643],[567,1428,1274],{"className":1429,"style":1300},[618,643],[567,1431,1435,1438],{"className":1432,"style":1434},[1433],"svg-align","top:-3.6833em;",[567,1436],{"className":1437,"style":639},[638],[567,1439,1443],{"className":1440,"style":1442},[1441],"hide-tail","height:0.522em;min-width:0.888em;",[660,1444,1449],{"xmlns":662,"width":1445,"height":1446,"viewBox":1447,"preserveAspectRatio":1448},"400em","0.522em","0 0 400000 522","xMaxYMin slice",[669,1450],{"d":1451},"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",[567,1453,1455,1485],{"className":1454},[570],[567,1456,1458],{"className":1457},[574],[576,1459,1460],{"xmlns":578},[580,1461,1462,1482],{},[583,1463,1464,1470,1472],{},[586,1465,1466,1468],{"accent":588},[590,1467,689],{},[594,1469,596],{},[594,1471,787],{},[586,1473,1474,1480],{"accent":588},[583,1475,1476,1478],{},[590,1477,1271],{},[590,1479,1280],{},[594,1481,1340],{"stretchy":588},[598,1483,1484],{"encoding":600},"\\vec{b} = \\overrightarrow{AD}",[567,1486,1488,1538],{"className":1487,"ariaHidden":588},[605],[567,1489,1491,1494,1529,1532,1535],{"className":1490},[609],[567,1492],{"className":1493,"style":704},[613],[567,1495,1497],{"className":1496},[618,619],[567,1498,1500],{"className":1499},[623],[567,1501,1503],{"className":1502},[627],[567,1504,1506,1514],{"className":1505,"style":704},[631],[567,1507,1508,1511],{"style":634},[567,1509],{"className":1510,"style":639},[638],[567,1512,689],{"className":1513},[618,643],[567,1515,1516,1519],{"style":727},[567,1517],{"className":1518,"style":639},[638],[567,1520,1522],{"className":1521,"style":653},[652],[567,1523,1525],{"className":1524,"style":658},[657],[660,1526,1527],{"xmlns":662,"width":663,"height":664,"style":665,"viewBox":666,"preserveAspectRatio":667},[669,1528],{"d":671},[567,1530],{"className":1531,"style":936},[879],[567,1533,787],{"className":1534},[940],[567,1536],{"className":1537,"style":936},[879],[567,1539,1541,1544],{"className":1540},[609],[567,1542],{"className":1543,"style":1403},[613],[567,1545,1547],{"className":1546},[618,619],[567,1548,1550],{"className":1549},[623],[567,1551,1553],{"className":1552},[627],[567,1554,1556,1570],{"className":1555,"style":1403},[631],[567,1557,1558,1561],{"style":634},[567,1559],{"className":1560,"style":639},[638],[567,1562,1564,1567],{"className":1563},[618],[567,1565,1271],{"className":1566},[618,643],[567,1568,1280],{"className":1569,"style":1308},[618,643],[567,1571,1573,1576],{"className":1572,"style":1434},[1433],[567,1574],{"className":1575,"style":639},[638],[567,1577,1579],{"className":1578,"style":1442},[1441],[660,1580,1581],{"xmlns":662,"width":1445,"height":1446,"viewBox":1447,"preserveAspectRatio":1448},[669,1582],{"d":1451},", also zwei Seiten, die an derselben Ecke anliegen.",[563,1585,1586,1587,1618,1619,1253],{},"Liegen die Vektoren in der Ebene, ergänzt man die dritte Koordinate ",[567,1588,1590,1605],{"className":1589},[570],[567,1591,1593],{"className":1592},[574],[576,1594,1595],{"xmlns":578},[580,1596,1597,1603],{},[583,1598,1599],{},[1600,1601,1602],"mn",{},"0",[598,1604,1602],{"encoding":600},[567,1606,1608],{"className":1607,"ariaHidden":588},[605],[567,1609,1611,1615],{"className":1610},[609],[567,1612],{"className":1613,"style":1614},[613],"height:0.6444em;",[567,1616,1602],{"className":1617},[618],". Dann bleibt nur ",[567,1620,1622,1673],{"className":1621},[570],[567,1623,1625],{"className":1624},[574],[576,1626,1627],{"xmlns":578},[580,1628,1629,1670],{},[583,1630,1631,1634,1636,1638,1646,1653,1656,1662,1668],{},[590,1632,1633],{},"F",[594,1635,787],{},[590,1637,767],{"mathvariant":766},[1639,1640,1641,1643],"msub",{},[590,1642,592],{},[1600,1644,1645],{},"1",[1639,1647,1648,1650],{},[590,1649,689],{},[1600,1651,1652],{},"2",[594,1654,1655],{},"−",[1639,1657,1658,1660],{},[590,1659,592],{},[1600,1661,1652],{},[1639,1663,1664,1666],{},[590,1665,689],{},[1600,1667,1645],{},[590,1669,767],{"mathvariant":766},[598,1671,1672],{"encoding":600},"F = |a_1 b_2 - a_2 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= (3,\\ 0,\\ 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= (1,\\ 2,\\ 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liegen in der ",[567,2176,2178,2203],{"className":2177},[570],[567,2179,2181],{"className":2180},[574],[576,2182,2183],{"xmlns":578},[580,2184,2185,2200],{},[583,2186,2187,2194],{},[1639,2188,2189,2192],{},[590,2190,2191],{},"x",[1600,2193,1645],{},[1639,2195,2196,2198],{},[590,2197,2191],{},[1600,2199,1652],{},[598,2201,2202],{"encoding":600},"x_1 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\\times \\vec{b} = \\begin{pmatrix} 0 \\\\ 0 \\\\ 3 \\cdot 2 - 0 \\cdot 1 \\end{pmatrix} = \\begin{pmatrix} 0 \\\\ 0 \\\\ 6 \\end{pmatrix}\n\\quad\\Rightarrow\\quad F = 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,[567,2833,2835],{"className":2834},[618],[567,2836,2410],{"className":2837},[618],[567,2839,1746],{"className":2840},[1745],[567,2842,2844],{"className":2843},[627],[567,2845,2847],{"className":2846,"style":2589},[631],[567,2848],{},[567,2850,2852],{"className":2851},[2040],[567,2853,2855],{"className":2854},[2550,2551],[567,2856,2858,2878],{"className":2857},[623,1717],[567,2859,2861,2875],{"className":2860},[627],[567,2862,2864],{"className":2863,"style":2561},[631],[567,2865,2866,2869],{"style":2564},[567,2867],{"className":2868,"style":2568},[638],[567,2870,2871],{"style":2571},[660,2872,2873],{"xmlns":662,"width":2574,"height":2575,"viewBox":2576},[669,2874],{"d":2720},[567,2876,1746],{"className":2877},[1745],[567,2879,2881],{"className":2880},[627],[567,2882,2884],{"className":2883,"style":2589},[631],[567,2885],{},[567,2887],{"className":2888,"style":2889},[879],"margin-right:1em;",[567,2891],{"className":2892,"style":936},[879],[567,2894,2417],{"className":2895},[940],[567,2897],{"className":2898,"style":2889},[879],[567,2900],{"className":2901,"style":936},[879],[567,2903,2905,2908,2911,2914,2917],{"className":2904},[609],[567,2906],{"className":2907,"style":1293},[613],[567,2909,1633],{"className":2910,"style":1685},[618,643],[567,2912],{"className":2913,"style":936},[879],[567,2915,787],{"className":2916},[940],[567,2918],{"className":2919,"style":936},[879],[567,2921,2923,2926],{"className":2922},[609],[567,2924],{"className":2925,"style":1614},[613],[567,2927,2410],{"className":2928},[618],[563,2930,2931,2932,2960,2961,2989,2990,1253],{},"Probe: Grundseite ",[567,2933,2935,2948],{"className":2934},[570],[567,2936,2938],{"className":2937},[574],[576,2939,2940],{"xmlns":578},[580,2941,2942,2946],{},[583,2943,2944],{},[1600,2945,1926],{},[598,2947,1926],{"encoding":600},[567,2949,2951],{"className":2950,"ariaHidden":588},[605],[567,2952,2954,2957],{"className":2953},[609],[567,2955],{"className":2956,"style":1614},[613],[567,2958,1926],{"className":2959},[618],", Höhe ",[567,2962,2964,2977],{"className":2963},[570],[567,2965,2967],{"className":2966},[574],[576,2968,2969],{"xmlns":578},[580,2970,2971,2975],{},[583,2972,2973],{},[1600,2974,1652],{},[598,2976,1652],{"encoding":600},[567,2978,2980],{"className":2979,"ariaHidden":588},[605],[567,2981,2983,2986],{"className":2982},[609],[567,2984],{"className":2985,"style":1614},[613],[567,2987,1652],{"className":2988},[618],", also ",[567,2991,2993,3015],{"className":2992},[570],[567,2994,2996],{"className":2995},[574],[576,2997,2998],{"xmlns":578},[580,2999,3000,3012],{},[583,3001,3002,3004,3006,3008,3010],{},[1600,3003,1926],{},[594,3005,800],{},[1600,3007,1652],{},[594,3009,787],{},[1600,3011,2410],{},[598,3013,3014],{"encoding":600},"3 \\cdot 2 = 6",[567,3016,3018,3036,3054],{"className":3017,"ariaHidden":588},[605],[567,3019,3021,3024,3027,3030,3033],{"className":3020},[609],[567,3022],{"className":3023,"style":1614},[613],[567,3025,1926],{"className":3026},[618],[567,3028],{"className":3029,"style":880},[879],[567,3031,800],{"className":3032},[884],[567,3034],{"className":3035,"style":880},[879],[567,3037,3039,3042,3045,3048,3051],{"className":3038},[609],[567,3040],{"className":3041,"style":1614},[613],[567,3043,1652],{"className":3044},[618],[567,3046],{"className":3047,"style":936},[879],[567,3049,787],{"className":3050},[940],[567,3052],{"className":3053,"style":936},[879],[567,3055,3057,3060],{"className":3056},[609],[567,3058],{"className":3059,"style":1614},[613],[567,3061,2410],{"className":3062},[618],[563,3064,3065,3066,672,3199,3332],{},"Für ",[567,3067,3069,3107],{"className":3068},[570],[567,3070,3072],{"className":3071},[574],[576,3073,3074],{"xmlns":578},[580,3075,3076,3104],{},[583,3077,3078,3084,3086,3088,3090,3092,3094,3096,3098,3100,3102],{},[586,3079,3080,3082],{"accent":588},[590,3081,592],{},[594,3083,596],{},[594,3085,787],{},[594,3087,1923],{"stretchy":1922},[1600,3089,1645],{},[594,3091,824],{"separator":588},[1930,3093,1932],{},[1600,3095,1652],{},[594,3097,824],{"separator":588},[1930,3099,1932],{},[1600,3101,1652],{},[594,3103,1943],{"stretchy":1922},[598,3105,3106],{"encoding":600},"\\vec{a} = (1,\\ 2,\\ 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= (2,\\ 0,\\ 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\\times \\vec{b} = \\begin{pmatrix} 2 \\cdot 1 - 2 \\cdot 0 \\\\ 2 \\cdot 2 - 1 \\cdot 1 \\\\ 1 \\cdot 0 - 2 \\cdot 2 \\end{pmatrix} = \\begin{pmatrix} 2 \\\\ 3 \\\\ -4 \\end{pmatrix}\n\\quad\\Rightarrow\\quad F = \\sqrt{4 + 9 + 16} = \\sqrt{29} \\approx 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80h400000v40h-400000z",[567,4144,1746],{"className":4145},[1745],[567,4147,4149],{"className":4148},[627],[567,4150,4153],{"className":4151,"style":4152},[631],"height:0.1256em;",[567,4154],{},[567,4156],{"className":4157,"style":936},[879],[567,4159,787],{"className":4160},[940],[567,4162],{"className":4163,"style":936},[879],[567,4165,4167,4171,4221,4224,4227],{"className":4166},[609],[567,4168],{"className":4169,"style":4170},[613],"height:1.04em;vertical-align:-0.0839em;",[567,4172,4174],{"className":4173},[618,4077],[567,4175,4177,4212],{"className":4176},[623,1717],[567,4178,4180,4209],{"className":4179},[627],[567,4181,4184,4196],{"className":4182,"style":4183},[631],"height:0.9561em;",[567,4185,4187,4190],{"className":4186,"style":634},[1433],[567,4188],{"className":4189,"style":639},[638],[567,4191,4193],{"className":4192,"style":4097},[618],[567,4194,3511],{"className":4195},[618],[567,4197,4199,4202],{"style":4198},"top:-2.9161em;",[567,4200],{"className":4201,"style":639},[638],[567,4203,4205],{"className":4204,"style":4134},[1441],[660,4206,4207],{"xmlns":662,"width":1445,"height":4137,"viewBox":4138,"preserveAspectRatio":4139},[669,4208],{"d":4142},[567,4210,1746],{"className":4211},[1745],[567,4213,4215],{"className":4214},[627],[567,4216,4219],{"className":4217,"style":4218},[631],"height:0.0839em;",[567,4220],{},[567,4222],{"className":4223,"style":936},[879],[567,4225,3514],{"className":4226},[940],[567,4228],{"className":4229,"style":936},[879],[567,4231,4233,4237,4241,4247],{"className":4232},[609],[567,4234],{"className":4235,"style":4236},[613],"height:0.8389em;vertical-align:-0.1944em;",[567,4238,4240],{"className":4239},[618],"5",[567,4242,4244],{"className":4243},[618],[567,4245,824],{"className":4246},[1077],[567,4248,4250],{"className":4249},[618],"39",[558,4252,4254],{"id":4253},"typische-fehler","Typische Fehler",[4256,4257,4258,4386,4536],"ul",{},[4259,4260,4261,4262,4385],"li",{},"Den Betrag vergessen und den Vektor ",[567,4263,4265,4291],{"className":4264},[570],[567,4266,4268],{"className":4267},[574],[576,4269,4270],{"xmlns":578},[580,4271,4272,4288],{},[583,4273,4274,4280,4282],{},[586,4275,4276,4278],{"accent":588},[590,4277,592],{},[594,4279,596],{},[594,4281,776],{},[586,4283,4284,4286],{"accent":588},[590,4285,689],{},[594,4287,596],{},[598,4289,4290],{"encoding":600},"\\vec{a} \\times \\vec{b}",[567,4292,4294,4344],{"className":4293,"ariaHidden":588},[605],[567,4295,4297,4300,4335,4338,4341],{"className":4296},[609],[567,4298],{"className":4299,"style":2438},[613],[567,4301,4303],{"className":4302},[618,619],[567,4304,4306],{"className":4305},[623],[567,4307,4309],{"className":4308},[627],[567,4310,4312,4320],{"className":4311,"style":614},[631],[567,4313,4314,4317],{"style":634},[567,4315],{"className":4316,"style":639},[638],[567,4318,592],{"className":4319},[618,643],[567,4321,4322,4325],{"style":634},[567,4323],{"className":4324,"style":639},[638],[567,4326,4328],{"className":4327,"style":653},[652],[567,4329,4331],{"className":4330,"style":658},[657],[660,4332,4333],{"xmlns":662,"width":663,"height":664,"style":665,"viewBox":666,"preserveAspectRatio":667},[669,4334],{"d":671},[567,4336],{"className":4337,"style":880},[879],[567,4339,776],{"className":4340},[884],[567,4342],{"className":4343,"style":880},[879],[567,4345,4347,4350],{"className":4346},[609],[567,4348],{"className":4349,"style":704},[613],[567,4351,4353],{"className":4352},[618,619],[567,4354,4356],{"className":4355},[623],[567,4357,4359],{"className":4358},[627],[567,4360,4362,4370],{"className":4361,"style":704},[631],[567,4363,4364,4367],{"style":634},[567,4365],{"className":4366,"style":639},[638],[567,4368,689],{"className":4369},[618,643],[567,4371,4372,4375],{"style":727},[567,4373],{"className":4374,"style":639},[638],[567,4376,4378],{"className":4377,"style":653},[652],[567,4379,4381],{"className":4380,"style":658},[657],[660,4382,4383],{"xmlns":662,"width":663,"height":664,"style":665,"viewBox":666,"preserveAspectRatio":667},[669,4384],{"d":671}," als Fläche angeben. Die Fläche ist eine Zahl.",[4259,4387,4388,4389,672,4462,4535],{},"Zwei gegenüberliegende Seiten verwenden, z.B. ",[567,4390,4392,4414],{"className":4391},[570],[567,4393,4395],{"className":4394},[574],[576,4396,4397],{"xmlns":578},[580,4398,4399,4411],{},[583,4400,4401],{},[586,4402,4403,4409],{"accent":588},[583,4404,4405,4407],{},[590,4406,1271],{},[590,4408,1274],{},[594,4410,1340],{"stretchy":588},[598,4412,4413],{"encoding":600},"\\overrightarrow{AB}",[567,4415,4417],{"className":4416,"ariaHidden":588},[605],[567,4418,4420,4423],{"className":4419},[609],[567,4421],{"className":4422,"style":1403},[613],[567,4424,4426],{"className":4425},[618,619],[567,4427,4429],{"className":4428},[623],[567,4430,4432],{"className":4431},[627],[567,4433,4435,4449],{"className":4434,"style":1403},[631],[567,4436,4437,4440],{"style":634},[567,4438],{"className":4439,"style":639},[638],[567,4441,4443,4446],{"className":4442},[618],[567,4444,1271],{"className":4445},[618,643],[567,4447,1274],{"className":4448,"style":1300},[618,643],[567,4450,4452,4455],{"className":4451,"style":1434},[1433],[567,4453],{"className":4454,"style":639},[638],[567,4456,4458],{"className":4457,"style":1442},[1441],[660,4459,4460],{"xmlns":662,"width":1445,"height":1446,"viewBox":1447,"preserveAspectRatio":1448},[669,4461],{"d":1451},[567,4463,4465,4487],{"className":4464},[570],[567,4466,4468],{"className":4467},[574],[576,4469,4470],{"xmlns":578},[580,4471,4472,4484],{},[583,4473,4474],{},[586,4475,4476,4482],{"accent":588},[583,4477,4478,4480],{},[590,4479,1280],{},[590,4481,1277],{},[594,4483,1340],{"stretchy":588},[598,4485,4486],{"encoding":600},"\\overrightarrow{DC}",[567,4488,4490],{"className":4489,"ariaHidden":588},[605],[567,4491,4493,4496],{"className":4492},[609],[567,4494],{"className":4495,"style":1403},[613],[567,4497,4499],{"className":4498},[618,619],[567,4500,4502],{"className":4501},[623],[567,4503,4505],{"className":4504},[627],[567,4506,4508,4522],{"className":4507,"style":1403},[631],[567,4509,4510,4513],{"style":634},[567,4511],{"className":4512,"style":639},[638],[567,4514,4516,4519],{"className":4515},[618],[567,4517,1280],{"className":4518,"style":1308},[618,643],[567,4520,1277],{"className":4521,"style":1304},[618,643],[567,4523,4525,4528],{"className":4524,"style":1434},[1433],[567,4526],{"className":4527,"style":639},[638],[567,4529,4531],{"className":4530,"style":1442},[1441],[660,4532,4533],{"xmlns":662,"width":1445,"height":1446,"viewBox":1447,"preserveAspectRatio":1448},[669,4534],{"d":1451},". Die sind parallel, das Kreuzprodukt wäre der Nullvektor.",[4259,4537,4538],{},"Die Diagonale statt einer Seite verwenden. Dann erhält man die Fläche eines anderen Parallelogramms.",{"title":4540,"searchDepth":4541,"depth":4541,"links":4542},"",2,[4543,4544,4545],{"id":560,"depth":4541,"text":561},{"id":1896,"depth":4541,"text":1897},{"id":4253,"depth":4541,"text":4254},[4547,4550,4553,4555,4557,4559,4561,4564,4567],{"lhs":4548,"rhs":4549},"(a2*b3 - a3*b2)^2 + (a3*b1 - a1*b3)^2 + (a1*b2 - a2*b1)^2","(a1^2 + a2^2 + a3^2)*(b1^2 + b2^2 + b3^2) - (a1*b1 + a2*b2 + a3*b3)^2",{"lhs":4551,"rhs":4552},"sqrt(0^2 + 0^2 + (a1*b2 - a2*b1)^2)","abs(a1*b2 - a2*b1)",{"lhs":4554,"rhs":2410},"3*2 - 0*1",{"lhs":4556,"rhs":2410},"3 * 2",{"lhs":4558,"rhs":1652},"2*1 - 2*0",{"lhs":4560,"rhs":1926},"2*2 - 1*1",{"lhs":4562,"rhs":4563},"1*0 - 2*2","-4",{"lhs":4565,"rhs":4566},"sqrt(2^2 + 3^2 + (-4)^2)","sqrt(29)",{"lhs":4568,"rhs":4569},"round(sqrt(29), 2)","5.39","\\vec{a}, \\vec{b} \\in \\mathbb{R}^3","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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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 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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:0.8141em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","parallelogram-area-vectors","F = |\\vec{a} \\times \\vec{b}|","\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>F\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>×\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F = |\\vec{a} \\times \\vec{b}|\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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\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: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 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