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\\vec{0}",[596,979,981,1068,1155],{"className":980,"ariaHidden":626},[625],[596,982,984,987,1059,1062,1065],{"className":983},[630],[596,985],{"className":986,"style":712},[634],[596,988,990,1025],{"className":989},[639],[596,991,993],{"className":992},[639,719],[596,994,996],{"className":995},[723],[596,997,999],{"className":998},[727],[596,1000,1002,1010],{"className":1001,"style":732},[731],[596,1003,1004,1007],{"style":735},[596,1005],{"className":1006,"style":740},[739],[596,1008,671],{"className":1009},[639,640],[596,1011,1012,1015],{"style":735},[596,1013],{"className":1014,"style":740},[739],[596,1016,1018],{"className":1017,"style":753},[752],[596,1019,1021],{"className":1020,"style":758},[757],[760,1022,1023],{"xmlns":762,"width":763,"height":764,"style":765,"viewBox":766,"preserveAspectRatio":767},[769,1024],{"d":771},[596,1026,1028],{"className":1027},[775],[596,1029,1031,1051],{"className":1030},[723,779],[596,1032,1034,1048],{"className":1033},[727],[596,1035,1037],{"className":1036,"style":786},[731],[596,1038,1039,1042],{"style":789},[596,1040],{"className":1041,"style":793},[739],[596,1043,1045],{"className":1044},[797,798,799,800],[596,1046,699],{"className":1047},[639,800],[596,1049,808],{"className":1050},[807],[596,1052,1054],{"className":1053},[727],[596,1055,1057],{"className":1056,"style":815},[731],[596,1058],{},[596,1060],{"className":1061,"style":844},[821],[596,1063,955],{"className":1064},[848],[596,1066],{"className":1067,"style":844},[821],[596,1069,1071,1074,1146,1149,1152],{"className":1070},[630],[596,1072],{"className":1073,"style":712},[634],[596,1075,1077,1112],{"className":1076},[639],[596,1078,1080],{"className":1079},[639,719],[596,1081,1083],{"className":1082},[723],[596,1084,1086],{"className":1085},[727],[596,1087,1089,1097],{"className":1088,"style":732},[731],[596,1090,1091,1094],{"style":735},[596,1092],{"className":1093,"style":740},[739],[596,1095,671],{"className":1096},[639,640],[596,1098,1099,1102],{"style":735},[596,1100],{"className":1101,"style":740},[739],[596,1103,1105],{"className":1104,"style":753},[752],[596,1106,1108],{"className":1107,"style":758},[757],[760,1109,1110],{"xmlns":762,"width":763,"height":764,"style":765,"viewBox":766,"preserveAspectRatio":767},[769,1111],{"d":771},[596,1113,1115],{"className":1114},[775],[596,1116,1118,1138],{"className":1117},[723,779],[596,1119,1121,1135],{"className":1120},[727],[596,1122,1124],{"className":1123,"style":786},[731],[596,1125,1126,1129],{"style":789},[596,1127],{"className":1128,"style":793},[739],[596,1130,1132],{"className":1131},[797,798,799,800],[596,1133,679],{"className":1134},[639,800],[596,1136,808],{"className":1137},[807],[596,1139,1141],{"className":1140},[727],[596,1142,1144],{"className":1143,"style":815},[731],[596,1145],{},[596,1147],{"className":1148,"style":822},[821],[596,1150,682],{"className":1151},[826],[596,1153],{"className":1154,"style":822},[821],[596,1156,1158,1162],{"className":1157},[630],[596,1159],{"className":1160,"style":1161},[634],"height:0.9274em;",[596,1163,1165],{"className":1164},[639,719],[596,1166,1168],{"className":1167},[723],[596,1169,1171],{"className":1170},[727],[596,1172,1174,1182],{"className":1173,"style":1161},[731],[596,1175,1176,1179],{"style":735},[596,1177],{"className":1178,"style":740},[739],[596,1180,972],{"className":1181},[639],[596,1183,1185,1188],{"style":1184},"top:-3.2134em;",[596,1186],{"className":1187,"style":740},[739],[596,1189,1191],{"className":1190,"style":753},[752],[596,1192,1194],{"className":1193,"style":758},[757],[760,1195,1196],{"xmlns":762,"width":763,"height":764,"style":765,"viewBox":766,"preserveAspectRatio":767},[769,1197],{"d":771},"), sind die Ebenen parallel. Man multipliziert die Gleichung von ",[596,1200,1202,1221],{"className":1201},[599],[596,1203,1205],{"className":1204},[603],[605,1206,1207],{"xmlns":607},[609,1208,1209,1218],{},[612,1210,1211],{},[664,1212,1213,1216],{},[615,1214,1215],{},"E",[677,1217,699],{},[619,1219,1220],{"encoding":621},"E_1",[596,1222,1224],{"className":1223,"ariaHidden":626},[625],[596,1225,1227,1231],{"className":1226},[630],[596,1228],{"className":1229,"style":1230},[634],"height:0.8333em;vertical-align:-0.15em;",[596,1232,1234,1238],{"className":1233},[639],[596,1235,1215],{"className":1236,"style":1237},[639,640],"margin-right:0.0576em;",[596,1239,1241],{"className":1240},[775],[596,1242,1244,1265],{"className":1243},[723,779],[596,1245,1247,1262],{"className":1246},[727],[596,1248,1250],{"className":1249,"style":786},[731],[596,1251,1253,1256],{"style":1252},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[596,1254],{"className":1255,"style":793},[739],[596,1257,1259],{"className":1258},[797,798,799,800],[596,1260,699],{"className":1261},[639,800],[596,1263,808],{"className":1264},[807],[596,1266,1268],{"className":1267},[727],[596,1269,1271],{"className":1270,"style":815},[731],[596,1272],{}," mit ",[596,1275,1277,1290],{"className":1276},[599],[596,1278,1280],{"className":1279},[603],[605,1281,1282],{"xmlns":607},[609,1283,1284,1288],{},[612,1285,1286],{},[615,1287,685],{},[619,1289,685],{"encoding":621},[596,1291,1293],{"className":1292,"ariaHidden":626},[625],[596,1294,1296,1299],{"className":1295},[630],[596,1297],{"className":1298,"style":836},[634],[596,1300,685],{"className":1301,"style":840},[639,640],": Stimmt dann auch die rechte Seite mit ",[596,1304,1306,1325],{"className":1305},[599],[596,1307,1309],{"className":1308},[603],[605,1310,1311],{"xmlns":607},[609,1312,1313,1322],{},[612,1314,1315],{},[664,1316,1317,1320],{},[615,1318,1319],{},"d",[677,1321,679],{},[619,1323,1324],{"encoding":621},"d_2",[596,1326,1328],{"className":1327,"ariaHidden":626},[625],[596,1329,1331,1335],{"className":1330},[630],[596,1332],{"className":1333,"style":1334},[634],"height:0.8444em;vertical-align:-0.15em;",[596,1336,1338,1341],{"className":1337},[639],[596,1339,1319],{"className":1340},[639,640],[596,1342,1344],{"className":1343},[775],[596,1345,1347,1367],{"className":1346},[723,779],[596,1348,1350,1364],{"className":1349},[727],[596,1351,1353],{"className":1352,"style":786},[731],[596,1354,1355,1358],{"style":789},[596,1356],{"className":1357,"style":793},[739],[596,1359,1361],{"className":1360},[797,798,799,800],[596,1362,679],{"className":1363},[639,800],[596,1365,808],{"className":1366},[807],[596,1368,1370],{"className":1369},[727],[596,1371,1373],{"className":1372,"style":815},[731],[596,1374],{}," überein, sind die Ebenen identisch, sonst echt parallel.",[572,1377,1378,1379,1584],{},"Sonst schneiden sie sich. Die Schnittgerade steht auf beiden Normalenvektoren senkrecht, also ist ",[596,1380,1382,1416],{"className":1381},[599],[596,1383,1385],{"className":1384},[603],[605,1386,1387],{"xmlns":607},[609,1388,1389,1413],{},[612,1390,1391,1401,1403],{},[664,1392,1393,1399],{},[667,1394,1395,1397],{"accent":626},[615,1396,671],{},[673,1398,675],{},[677,1400,699],{},[673,1402,955],{},[664,1404,1405,1411],{},[667,1406,1407,1409],{"accent":626},[615,1408,671],{},[673,1410,675],{},[677,1412,679],{},[619,1414,1415],{"encoding":621},"\\vec{n}_1 \\times \\vec{n}_2",[596,1417,1419,1506],{"className":1418,"ariaHidden":626},[625],[596,1420,1422,1425,1497,1500,1503],{"className":1421},[630],[596,1423],{"className":1424,"style":712},[634],[596,1426,1428,1463],{"className":1427},[639],[596,1429,1431],{"className":1430},[639,719],[596,1432,1434],{"className":1433},[723],[596,1435,1437],{"className":1436},[727],[596,1438,1440,1448],{"className":1439,"style":732},[731],[596,1441,1442,1445],{"style":735},[596,1443],{"className":1444,"style":740},[739],[596,1446,671],{"className":1447},[639,640],[596,1449,1450,1453],{"style":735},[596,1451],{"className":1452,"style":740},[739],[596,1454,1456],{"className":1455,"style":753},[752],[596,1457,1459],{"className":1458,"style":758},[757],[760,1460,1461],{"xmlns":762,"width":763,"height":764,"style":765,"viewBox":766,"preserveAspectRatio":767},[769,1462],{"d":771},[596,1464,1466],{"className":1465},[775],[596,1467,1469,1489],{"className":1468},[723,779],[596,1470,1472,1486],{"className":1471},[727],[596,1473,1475],{"className":1474,"style":786},[731],[596,1476,1477,1480],{"style":789},[596,1478],{"className":1479,"style":793},[739],[596,1481,1483],{"className":1482},[797,798,799,800],[596,1484,699],{"className":1485},[639,800],[596,1487,808],{"className":1488},[807],[596,1490,1492],{"className":1491},[727],[596,1493,1495],{"className":1494,"style":815},[731],[596,1496],{},[596,1498],{"className":1499,"style":844},[821],[596,1501,955],{"className":1502},[848],[596,1504],{"className":1505,"style":844},[821],[596,1507,1509,1512],{"className":1508},[630],[596,1510],{"className":1511,"style":712},[634],[596,1513,1515,1550],{"className":1514},[639],[596,1516,1518],{"className":1517},[639,719],[596,1519,1521],{"className":1520},[723],[596,1522,1524],{"className":1523},[727],[596,1525,1527,1535],{"className":1526,"style":732},[731],[596,1528,1529,1532],{"style":735},[596,1530],{"className":1531,"style":740},[739],[596,1533,671],{"className":1534},[639,640],[596,1536,1537,1540],{"style":735},[596,1538],{"className":1539,"style":740},[739],[596,1541,1543],{"className":1542,"style":753},[752],[596,1544,1546],{"className":1545,"style":758},[757],[760,1547,1548],{"xmlns":762,"width":763,"height":764,"style":765,"viewBox":766,"preserveAspectRatio":767},[769,1549],{"d":771},[596,1551,1553],{"className":1552},[775],[596,1554,1556,1576],{"className":1555},[723,779],[596,1557,1559,1573],{"className":1558},[727],[596,1560,1562],{"className":1561,"style":786},[731],[596,1563,1564,1567],{"style":789},[596,1565],{"className":1566,"style":793},[739],[596,1568,1570],{"className":1569},[797,798,799,800],[596,1571,679],{"className":1572},[639,800],[596,1574,808],{"className":1575},[807],[596,1577,1579],{"className":1578},[727],[596,1580,1582],{"className":1581,"style":815},[731],[596,1583],{}," ein Richtungsvektor. Einen Stützpunkt findet man, indem man eine Koordinate frei wählt und das Gleichungssystem aus beiden Ebenengleichungen löst.",[565,1586,1587],{},"Alternativ löst man das Gleichungssystem aus beiden Koordinatenformen direkt mit einem Parameter. Das liefert die Schnittgerade ebenfalls.",[560,1589,1591],{"id":1590},"beispiele","Beispiele",[565,1593,1594,1913,1914,2152,2153,1913,2236,2316],{},[596,1595,1597,1663],{"className":1596},[599],[596,1598,1600],{"className":1599},[603],[605,1601,1602],{"xmlns":607},[609,1603,1604,1660],{},[612,1605,1606,1612,1614,1617,1621,1625,1628,1631,1638,1641,1647,1649,1656,1658],{},[664,1607,1608,1610],{},[615,1609,1215],{},[677,1611,699],{},[821,1613],{},[821,1615],{"width":1616},"0.1111em",[673,1618],{"lspace":1619,"rspace":1620},"0em","0.17em",[1622,1623,1624],"mtext",{}," ⁣",[673,1626,1627],{"lspace":1619,"rspace":1619},":",[821,1629],{"width":1630},"0.3333em",[664,1632,1633,1636],{},[615,1634,1635],{},"x",[677,1637,699],{},[673,1639,1640],{},"+",[664,1642,1643,1645],{},[615,1644,1635],{},[677,1646,679],{},[673,1648,1640],{},[664,1650,1651,1653],{},[615,1652,1635],{},[677,1654,1655],{},"3",[673,1657,682],{},[677,1659,1655],{},[619,1661,1662],{"encoding":621},"E_1\\colon x_1 + x_2 + x_3 = 3",[596,1664,1666,1791,1847,1903],{"className":1665,"ariaHidden":626},[625],[596,1667,1669,1672,1712,1716,1720,1724,1728,1732,1738,1742,1782,1785,1788],{"className":1668},[630],[596,1670],{"className":1671,"style":1230},[634],[596,1673,1675,1678],{"className":1674},[639],[596,1676,1215],{"className":1677,"style":1237},[639,640],[596,1679,1681],{"className":1680},[775],[596,1682,1684,1704],{"className":1683},[723,779],[596,1685,1687,1701],{"className":1686},[727],[596,1688,1690],{"className":1689,"style":786},[731],[596,1691,1692,1695],{"style":1252},[596,1693],{"className":1694,"style":793},[739],[596,1696,1698],{"className":1697},[797,798,799,800],[596,1699,699],{"className":1700},[639,800],[596,1702,808],{"className":1703},[807],[596,1705,1707],{"className":1706},[727],[596,1708,1710],{"className":1709,"style":815},[731],[596,1711],{},[596,1713],{"className":1714},[821,1715],"nobreak",[596,1717],{"className":1718,"style":1719},[821],"margin-right:0.1111em;",[596,1721],{"className":1722},[1723],"mpunct",[596,1725],{"className":1726,"style":1727},[821],"margin-right:-0.1667em;",[596,1729],{"className":1730,"style":1731},[821],"margin-right:0.1667em;",[596,1733,1735],{"className":1734},[639],[596,1736,1627],{"className":1737},[826],[596,1739],{"className":1740,"style":1741},[821],"margin-right:0.3333em;",[596,1743,1745,1748],{"className":1744},[639],[596,1746,1635],{"className":1747},[639,640],[596,1749,1751],{"className":1750},[775],[596,1752,1754,1774],{"className":1753},[723,779],[596,1755,1757,1771],{"className":1756},[727],[596,1758,1760],{"className":1759,"style":786},[731],[596,1761,1762,1765],{"style":789},[596,1763],{"className":1764,"style":793},[739],[596,1766,1768],{"className":1767},[797,798,799,800],[596,1769,699],{"className":1770},[639,800],[596,1772,808],{"className":1773},[807],[596,1775,1777],{"className":1776},[727],[596,1778,1780],{"className":1779,"style":815},[731],[596,1781],{},[596,1783],{"className":1784,"style":844},[821],[596,1786,1640],{"className":1787},[848],[596,1789],{"className":1790,"style":844},[821],[596,1792,1794,1798,1838,1841,1844],{"className":1793},[630],[596,1795],{"className":1796,"style":1797},[634],"height:0.7333em;vertical-align:-0.15em;",[596,1799,1801,1804],{"className":1800},[639],[596,1802,1635],{"className":1803},[639,640],[596,1805,1807],{"className":1806},[775],[596,1808,1810,1830],{"className":1809},[723,779],[596,1811,1813,1827],{"className":1812},[727],[596,1814,1816],{"className":1815,"style":786},[731],[596,1817,1818,1821],{"style":789},[596,1819],{"className":1820,"style":793},[739],[596,1822,1824],{"className":1823},[797,798,799,800],[596,1825,679],{"className":1826},[639,800],[596,1828,808],{"className":1829},[807],[596,1831,1833],{"className":1832},[727],[596,1834,1836],{"className":1835,"style":815},[731],[596,1837],{},[596,1839],{"className":1840,"style":844},[821],[596,1842,1640],{"className":1843},[848],[596,1845],{"className":1846,"style":844},[821],[596,1848,1850,1854,1894,1897,1900],{"className":1849},[630],[596,1851],{"className":1852,"style":1853},[634],"height:0.5806em;vertical-align:-0.15em;",[596,1855,1857,1860],{"className":1856},[639],[596,1858,1635],{"className":1859},[639,640],[596,1861,1863],{"className":1862},[775],[596,1864,1866,1886],{"className":1865},[723,779],[596,1867,1869,1883],{"className":1868},[727],[596,1870,1872],{"className":1871,"style":786},[731],[596,1873,1874,1877],{"style":789},[596,1875],{"className":1876,"style":793},[739],[596,1878,1880],{"className":1879},[797,798,799,800],[596,1881,1655],{"className":1882},[639,800],[596,1884,808],{"className":1885},[807],[596,1887,1889],{"className":1888},[727],[596,1890,1892],{"className":1891,"style":815},[731],[596,1893],{},[596,1895],{"className":1896,"style":822},[821],[596,1898,682],{"className":1899},[826],[596,1901],{"className":1902,"style":822},[821],[596,1904,1906,1910],{"className":1905},[630],[596,1907],{"className":1908,"style":1909},[634],"height:0.6444em;",[596,1911,1655],{"className":1912},[639]," 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hat den Normalenvektor ",[596,4474,4476,4502],{"className":4475},[599],[596,4477,4479],{"className":4478},[603],[605,4480,4481],{"xmlns":607},[609,4482,4483,4499],{},[612,4484,4485,4487,4489],{},[677,4486,679],{},[673,4488,688],{},[664,4490,4491,4497],{},[667,4492,4493,4495],{"accent":626},[615,4494,671],{},[673,4496,675],{},[677,4498,699],{},[619,4500,4501],{"encoding":621},"2 \\cdot 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Verdoppelt man ",[596,4603,4605,4622],{"className":4604},[599],[596,4606,4608],{"className":4607},[603],[605,4609,4610],{"xmlns":607},[609,4611,4612,4620],{},[612,4613,4614],{},[664,4615,4616,4618],{},[615,4617,1215],{},[677,4619,699],{},[619,4621,1220],{"encoding":621},[596,4623,4625],{"className":4624,"ariaHidden":626},[625],[596,4626,4628,4631],{"className":4627},[630],[596,4629],{"className":4630,"style":1230},[634],[596,4632,4634,4637],{"className":4633},[639],[596,4635,1215],{"className":4636,"style":1237},[639,640],[596,4638,4640],{"className":4639},[775],[596,4641,4643,4663],{"className":4642},[723,779],[596,4644,4646,4660],{"className":4645},[727],[596,4647,4649],{"className":4648,"style":786},[731],[596,4650,4651,4654],{"style":1252},[596,4652],{"className":4653,"style":793},[739],[596,4655,4657],{"className":4656},[797,798,799,800],[596,4658,699],{"className":4659},[639,800],[596,4661,808],{"className":4662},[807],[596,4664,4666],{"className":4665},[727],[596,4667,4669],{"className":4668,"style":815},[731],[596,4670],{},", erhält man ",[596,4673,4675,4720],{"className":4674},[599],[596,4676,4678],{"className":4677},[603],[605,4679,4680],{"xmlns":607},[609,4681,4682,4717],{},[612,4683,4684,4686,4692,4694,4696,4702,4704,4706,4712,4714],{},[677,4685,679],{},[664,4687,4688,4690],{},[615,4689,1635],{},[677,4691,699],{},[673,4693,1640],{},[677,4695,679],{},[664,4697,4698,4700],{},[615,4699,1635],{},[677,4701,679],{},[673,4703,1640],{},[677,4705,679],{},[664,4707,4708,4710],{},[615,4709,1635],{},[677,4711,1655],{},[673,4713,682],{},[677,4715,4716],{},"6",[619,4718,4719],{"encoding":621},"2x_1 + 2x_2 + 2x_3 = 6",[596,4721,4723,4781,4839,4897],{"className":4722,"ariaHidden":626},[625],[596,4724,4726,4729,4732,4772,4775,4778],{"className":4725},[630],[596,4727],{"className":4728,"style":4352},[634],[596,4730,679],{"className":4731},[639],[596,4733,4735,4738],{"className":4734},[639],[596,4736,1635],{"className":4737},[639,640],[596,4739,4741],{"className":4740},[775],[596,4742,4744,4764],{"className":4743},[723,779],[596,4745,4747,4761],{"className":4746},[727],[596,4748,4750],{"className":4749,"style":786},[731],[596,4751,4752,4755],{"style":789},[596,4753],{"className":4754,"style":793},[739],[596,4756,4758],{"className":4757},[797,798,799,800],[596,4759,699],{"className":4760},[639,800],[596,4762,808],{"className":4763},[807],[596,4765,4767],{"className":4766},[727],[596,4768,4770],{"className":4769,"style":815},[731],[596,4771],{},[596,4773],{"className":4774,"style":844},[821],[596,4776,1640],{"className":4777},[848],[596,4779],{"className":4780,"style":844},[821],[596,4782,4784,4787,4790,4830,4833,4836],{"className":4783},[630],[596,4785],{"className":4786,"style":4352},[634],[596,4788,679],{"className":4789},[639],[596,4791,4793,4796],{"className":4792},[639],[596,4794,1635],{"className":4795},[639,640],[596,4797,4799],{"className":4798},[775],[596,4800,4802,4822],{"className":4801},[723,779],[596,4803,4805,4819],{"className":4804},[727],[596,4806,4808],{"className":4807,"style":786},[731],[596,4809,4810,4813],{"style":789},[596,4811],{"className":4812,"style":793},[739],[596,4814,4816],{"className":4815},[797,798,799,800],[596,4817,679],{"className":4818},[639,800],[596,4820,808],{"className":4821},[807],[596,4823,4825],{"className":4824},[727],[596,4826,4828],{"className":4827,"style":815},[731],[596,4829],{},[596,4831],{"className":4832,"style":844},[821],[596,4834,1640],{"className":4835},[848],[596,4837],{"className":4838,"style":844},[821],[596,4840,4842,4845,4848,4888,4891,4894],{"className":4841},[630],[596,4843],{"className":4844,"style":4352},[634],[596,4846,679],{"className":4847},[639],[596,4849,4851,4854],{"className":4850},[639],[596,4852,1635],{"className":4853},[639,640],[596,4855,4857],{"className":4856},[775],[596,4858,4860,4880],{"className":4859},[723,779],[596,4861,4863,4877],{"className":4862},[727],[596,4864,4866],{"className":4865,"style":786},[731],[596,4867,4868,4871],{"style":789},[596,4869],{"className":4870,"style":793},[739],[596,4872,4874],{"className":4873},[797,798,799,800],[596,4875,1655],{"className":4876},[639,800],[596,4878,808],{"className":4879},[807],[596,4881,4883],{"className":4882},[727],[596,4884,4886],{"className":4885,"style":815},[731],[596,4887],{},[596,4889],{"className":4890,"style":822},[821],[596,4892,682],{"className":4893},[826],[596,4895],{"className":4896,"style":822},[821],[596,4898,4900,4903],{"className":4899},[630],[596,4901],{"className":4902,"style":1909},[634],[596,4904,4716],{"className":4905},[639],". Wegen ",[596,4908,4910,4930],{"className":4909},[599],[596,4911,4913],{"className":4912},[603],[605,4914,4915],{"xmlns":607},[609,4916,4917,4927],{},[612,4918,4919,4921,4925],{},[677,4920,4716],{},[673,4922,4924],{"mathvariant":4923},"normal","≠",[677,4926,4217],{},[619,4928,4929],{"encoding":621},"6 \\neq 5",[596,4931,4933,4991],{"className":4932,"ariaHidden":626},[625],[596,4934,4936,4940,4943,4946,4988],{"className":4935},[630],[596,4937],{"className":4938,"style":4939},[634],"height:0.8889em;vertical-align:-0.1944em;",[596,4941,4716],{"className":4942},[639],[596,4944],{"className":4945,"style":822},[821],[596,4947,4949,4982,4985],{"className":4948},[826],[596,4950,4952],{"className":4951},[826],[596,4953,4956],{"className":4954},[639,4955],"vbox",[596,4957,4960],{"className":4958},[4959],"thinbox",[596,4961,4964,4967,4978],{"className":4962},[4963],"rlap",[596,4965],{"className":4966,"style":4939},[634],[596,4968,4971],{"className":4969},[4970],"inner",[596,4972,4974],{"className":4973},[639],[596,4975,4977],{"className":4976},[826],"",[596,4979],{"className":4980},[4981],"fix",[596,4983],{"className":4984},[821,1715],[596,4986,682],{"className":4987},[826],[596,4989],{"className":4990,"style":822},[821],[596,4992,4994,4997],{"className":4993},[630],[596,4995],{"className":4996,"style":1909},[634],[596,4998,4217],{"className":4999},[639]," sind ",[596,5002,5004,5021],{"className":5003},[599],[596,5005,5007],{"className":5006},[603],[605,5008,5009],{"xmlns":607},[609,5010,5011,5019],{},[612,5012,5013],{},[664,5014,5015,5017],{},[615,5016,1215],{},[677,5018,699],{},[619,5020,1220],{"encoding":621},[596,5022,5024],{"className":5023,"ariaHidden":626},[625],[596,5025,5027,5030],{"className":5026},[630],[596,5028],{"className":5029,"style":1230},[634],[596,5031,5033,5036],{"className":5032},[639],[596,5034,1215],{"className":5035,"style":1237},[639,640],[596,5037,5039],{"className":5038},[775],[596,5040,5042,5062],{"className":5041},[723,779],[596,5043,5045,5059],{"className":5044},[727],[596,5046,5048],{"className":5047,"style":786},[731],[596,5049,5050,5053],{"style":1252},[596,5051],{"className":5052,"style":793},[739],[596,5054,5056],{"className":5055},[797,798,799,800],[596,5057,699],{"className":5058},[639,800],[596,5060,808],{"className":5061},[807],[596,5063,5065],{"className":5064},[727],[596,5066,5068],{"className":5067,"style":815},[731],[596,5069],{},[596,5071,5073,5091],{"className":5072},[599],[596,5074,5076],{"className":5075},[603],[605,5077,5078],{"xmlns":607},[609,5079,5080,5088],{},[612,5081,5082],{},[664,5083,5084,5086],{},[615,5085,1215],{},[677,5087,1655],{},[619,5089,5090],{"encoding":621},"E_3",[596,5092,5094],{"className":5093,"ariaHidden":626},[625],[596,5095,5097,5100],{"className":5096},[630],[596,5098],{"className":5099,"style":1230},[634],[596,5101,5103,5106],{"className":5102},[639],[596,5104,1215],{"className":5105,"style":1237},[639,640],[596,5107,5109],{"className":5108},[775],[596,5110,5112,5132],{"className":5111},[723,779],[596,5113,5115,5129],{"className":5114},[727],[596,5116,5118],{"className":5117,"style":786},[731],[596,5119,5120,5123],{"style":1252},[596,5121],{"className":5122,"style":793},[739],[596,5124,5126],{"className":5125},[797,798,799,800],[596,5127,1655],{"className":5128},[639,800],[596,5130,808],{"className":5131},[807],[596,5133,5135],{"className":5134},[727],[596,5136,5138],{"className":5137,"style":815},[731],[596,5139],{}," echt parallel. Bei ",[596,5142,5144,5187],{"className":5143},[599],[596,5145,5147],{"className":5146},[603],[605,5148,5149],{"xmlns":607},[609,5150,5151,5185],{},[612,5152,5153,5155,5161,5163,5165,5171,5173,5175,5181,5183],{},[677,5154,679],{},[664,5156,5157,5159],{},[615,5158,1635],{},[677,5160,699],{},[673,5162,1640],{},[677,5164,679],{},[664,5166,5167,5169],{},[615,5168,1635],{},[677,5170,679],{},[673,5172,1640],{},[677,5174,679],{},[664,5176,5177,5179],{},[615,5178,1635],{},[677,5180,1655],{},[673,5182,682],{},[677,5184,4716],{},[619,5186,4719],{"encoding":621},[596,5188,5190,5248,5306,5364],{"className":5189,"ariaHidden":626},[625],[596,5191,5193,5196,5199,5239,5242,5245],{"className":5192},[630],[596,5194],{"className":5195,"style":4352},[634],[596,5197,679],{"className":5198},[639],[596,5200,5202,5205],{"className":5201},[639],[596,5203,1635],{"className":5204},[639,640],[596,5206,5208],{"className":5207},[775],[596,5209,5211,5231],{"className":5210},[723,779],[596,5212,5214,5228],{"className":5213},[727],[596,5215,5217],{"className":5216,"style":786},[731],[596,5218,5219,5222],{"style":789},[596,5220],{"className":5221,"style":793},[739],[596,5223,5225],{"className":5224},[797,798,799,800],[596,5226,699],{"className":5227},[639,800],[596,5229,808],{"className":5230},[807],[596,5232,5234],{"className":5233},[727],[596,5235,5237],{"className":5236,"style":815},[731],[596,5238],{},[596,5240],{"className":5241,"style":844},[821],[596,5243,1640],{"className":5244},[848],[596,5246],{"className":5247,"style":844},[821],[596,5249,5251,5254,5257,5297,5300,5303],{"className":5250},[630],[596,5252],{"className":5253,"style":4352},[634],[596,5255,679],{"className":5256},[639],[596,5258,5260,5263],{"className":5259},[639],[596,5261,1635],{"className":5262},[639,640],[596,5264,5266],{"className":5265},[775],[596,5267,5269,5289],{"className":5268},[723,779],[596,5270,5272,5286],{"className":5271},[727],[596,5273,5275],{"className":5274,"style":786},[731],[596,5276,5277,5280],{"style":789},[596,5278],{"className":5279,"style":793},[739],[596,5281,5283],{"className":5282},[797,798,799,800],[596,5284,679],{"className":5285},[639,800],[596,5287,808],{"className":5288},[807],[596,5290,5292],{"className":5291},[727],[596,5293,5295],{"className":5294,"style":815},[731],[596,5296],{},[596,5298],{"className":5299,"style":844},[821],[596,5301,1640],{"className":5302},[848],[596,5304],{"className":5305,"style":844},[821],[596,5307,5309,5312,5315,5355,5358,5361],{"className":5308},[630],[596,5310],{"className":5311,"style":4352},[634],[596,5313,679],{"className":5314},[639],[596,5316,5318,5321],{"className":5317},[639],[596,5319,1635],{"className":5320},[639,640],[596,5322,5324],{"className":5323},[775],[596,5325,5327,5347],{"className":5326},[723,779],[596,5328,5330,5344],{"className":5329},[727],[596,5331,5333],{"className":5332,"style":786},[731],[596,5334,5335,5338],{"style":789},[596,5336],{"className":5337,"style":793},[739],[596,5339,5341],{"className":5340},[797,798,799,800],[596,5342,1655],{"className":5343},[639,800],[596,5345,808],{"className":5346},[807],[596,5348,5350],{"className":5349},[727],[596,5351,5353],{"className":5352,"style":815},[731],[596,5354],{},[596,5356],{"className":5357,"style":822},[821],[596,5359,682],{"className":5360},[826],[596,5362],{"className":5363,"style":822},[821],[596,5365,5367,5370],{"className":5366},[630],[596,5368],{"className":5369,"style":1909},[634],[596,5371,4716],{"className":5372},[639]," wären sie identisch.",[560,5375,5377],{"id":5376},"typische-fehler","Typische Fehler",[569,5379,5380,5383,5386],{},[572,5381,5382],{},"Nur die Normalenvektoren vergleichen und dann „parallel\" und „identisch\" verwechseln. Die rechten Seiten müssen mit demselben Faktor verglichen werden.",[572,5384,5385],{},"Einen Normalenvektor als Richtungsvektor der Schnittgeraden nehmen. Die Schnittgerade steht senkrecht auf beiden Normalenvektoren.",[572,5387,5388,5389,5593],{},"Beim Stützpunkt eine Koordinate frei wählen, die auf der Schnittgeraden konstant ist, weil die passende Komponente von ",[596,5390,5392,5425],{"className":5391},[599],[596,5393,5395],{"className":5394},[603],[605,5396,5397],{"xmlns":607},[609,5398,5399,5423],{},[612,5400,5401,5411,5413],{},[664,5402,5403,5409],{},[667,5404,5405,5407],{"accent":626},[615,5406,671],{},[673,5408,675],{},[677,5410,699],{},[673,5412,955],{},[664,5414,5415,5421],{},[667,5416,5417,5419],{"accent":626},[615,5418,671],{},[673,5420,675],{},[677,5422,679],{},[619,5424,1415],{"encoding":621},[596,5426,5428,5515],{"className":5427,"ariaHidden":626},[625],[596,5429,5431,5434,5506,5509,5512],{"className":5430},[630],[596,5432],{"className":5433,"style":712},[634],[596,5435,5437,5472],{"className":5436},[639],[596,5438,5440],{"className":5439},[639,719],[596,5441,5443],{"className":5442},[723],[596,5444,5446],{"className":5445},[727],[596,5447,5449,5457],{"className":5448,"style":732},[731],[596,5450,5451,5454],{"style":735},[596,5452],{"className":5453,"style":740},[739],[596,5455,671],{"className":5456},[639,640],[596,5458,5459,5462],{"style":735},[596,5460],{"className":5461,"style":740},[739],[596,5463,5465],{"className":5464,"style":753},[752],[596,5466,5468],{"className":5467,"style":758},[757],[760,5469,5470],{"xmlns":762,"width":763,"height":764,"style":765,"viewBox":766,"preserveAspectRatio":767},[769,5471],{"d":771},[596,5473,5475],{"className":5474},[775],[596,5476,5478,5498],{"className":5477},[723,779],[596,5479,5481,5495],{"className":5480},[727],[596,5482,5484],{"className":5483,"style":786},[731],[596,5485,5486,5489],{"style":789},[596,5487],{"className":5488,"style":793},[739],[596,5490,5492],{"className":5491},[797,798,799,800],[596,5493,699],{"className":5494},[639,800],[596,5496,808],{"className":5497},[807],[596,5499,5501],{"className":5500},[727],[596,5502,5504],{"className":5503,"style":815},[731],[596,5505],{},[596,5507],{"className":5508,"style":844},[821],[596,5510,955],{"className":5511},[848],[596,5513],{"className":5514,"style":844},[821],[596,5516,5518,5521],{"className":5517},[630],[596,5519],{"className":5520,"style":712},[634],[596,5522,5524,5559],{"className":5523},[639],[596,5525,5527],{"className":5526},[639,719],[596,5528,5530],{"className":5529},[723],[596,5531,5533],{"className":5532},[727],[596,5534,5536,5544],{"className":5535,"style":732},[731],[596,5537,5538,5541],{"style":735},[596,5539],{"className":5540,"style":740},[739],[596,5542,671],{"className":5543},[639,640],[596,5545,5546,5549],{"style":735},[596,5547],{"className":5548,"style":740},[739],[596,5550,5552],{"className":5551,"style":753},[752],[596,5553,5555],{"className":5554,"style":758},[757],[760,5556,5557],{"xmlns":762,"width":763,"height":764,"style":765,"viewBox":766,"preserveAspectRatio":767},[769,5558],{"d":771},[596,5560,5562],{"className":5561},[775],[596,5563,5565,5585],{"className":5564},[723,779],[596,5566,5568,5582],{"className":5567},[727],[596,5569,5571],{"className":5570,"style":786},[731],[596,5572,5573,5576],{"style":789},[596,5574],{"className":5575,"style":793},[739],[596,5577,5579],{"className":5578},[797,798,799,800],[596,5580,679],{"className":5581},[639,800],[596,5583,808],{"className":5584},[807],[596,5586,5588],{"className":5587},[727],[596,5589,5591],{"className":5590,"style":815},[731],[596,5592],{}," null ist. Dann ist das System für den gewählten Wert meist unlösbar, und man muss eine andere Koordinate wählen.",{"title":5595,"searchDepth":5596,"depth":5596,"links":5597},"",2,[5598,5599,5600],{"id":562,"depth":5596,"text":563},{"id":1590,"depth":5596,"text":1591},{"id":5376,"depth":5596,"text":5377},[5602,5604,5606,5609,5611,5613,5615,5617],{"lhs":5603,"rhs":699},"cross([1, 1, 1], [1, -1, 0])[1]",{"lhs":5605,"rhs":699},"cross([1, 1, 1], [1, -1, 0])[2]",{"lhs":5607,"rhs":5608},"cross([1, 1, 1], [1, -1, 0])[3]","-2",{"lhs":5610,"rhs":1655},"1 + 0 + 2",{"lhs":5612,"rhs":699},"1 - 0",{"lhs":5614,"rhs":1655},"(1 + t) + t + (2 - 2*t)",{"lhs":5616,"rhs":699},"(1 + t) - t",{"lhs":5618,"rhs":4716},"2*3","E_1\\colon \\vec{n}_1 \\cdot \\vec{x} = d_1,\\ E_2\\colon \\vec{n}_2 \\cdot \\vec{x} = d_2,\\ \\vec{n}_1, \\vec{n}_2 \\neq \\vec{0}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>E\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\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>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>d\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E_1\\colon \\vec{n}_1 \\cdot \\vec{x} = 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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\">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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">d\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\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>\u003Cmsub>\u003Cmi>E\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\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>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmsub>\u003Cmi>d\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E_2\\colon \\vec{n}_2 \\cdot \\vec{x} = d_2,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.864em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" 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style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"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\">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 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmn>0\u003C\u002Fmn>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{n}_1, \\vec{n}_2 \\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\">\u003Cspan 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style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord 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\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"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:0.9274em;\">\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>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","plane-plane-position","\\vec{n}_1 \\times \\vec{n}_2 \\neq \\vec{0} \\;\\Rightarrow\\; E_1 \\cap E_2 = s \\text{ mit Richtungsvektor } \\vec{n}_1 \\times \\vec{n}_2","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>×\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmn>0\u003C\u002Fmn>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmsub>\u003Cmi>E\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>∩\u003C\u002Fmo>\u003Cmsub>\u003Cmi>E\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>s\u003C\u002Fmi>\u003Cmtext> mit Richtungsvektor \u003C\u002Fmtext>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>×\u003C\u002Fmo>\u003Cmsub>\u003Cmover accent=\"true\">\u003Cmi>n\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{n}_1 \\times \\vec{n}_2 \\neq \\vec{0} \\;\\Rightarrow\\; E_1 \\cap E_2 = s \\text{ mit Richtungsvektor } \\vec{n}_1 \\times 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