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Die rechte Seite ",[572,914,916,930],{"className":915},[575],[572,917,919],{"className":918},[579],[581,920,921],{"xmlns":583},[585,922,923,928],{},[588,924,925],{},[594,926,927],{},"d",[602,929,927],{"encoding":604},[572,931,933],{"className":932,"ariaHidden":610},[609],[572,934,936,940],{"className":935},[614],[572,937],{"className":938,"style":939},[618],"height:0.6944em;",[572,941,927],{"className":942},[623,627]," erhält man, indem man einen Punkt der Ebene einsetzt.",[563,945,946],{},"Die Koordinatenform ist für viele Aufgaben am praktischsten:",[948,949,950,957,963],"ul",{},[951,952,953,956],"li",{},[567,954,955],{},"Punktprobe",": Koordinaten einsetzen und prüfen, ob die Gleichung stimmt.",[951,958,959,962],{},[567,960,961],{},"Schnitt mit einer Geraden",": die Geradengleichung zeilenweise einsetzen und nach dem Parameter auflösen.",[951,964,965,968,969,999],{},[567,966,967],{},"Spurpunkte",": Schnittpunkte mit den Koordinatenachsen. Man setzt zwei Koordinaten ",[572,970,972,986],{"className":971},[575],[572,973,975],{"className":974},[579],[581,976,977],{"xmlns":583},[585,978,979,984],{},[588,980,981],{},[598,982,983],{},"0",[602,985,983],{"encoding":604},[572,987,989],{"className":988,"ariaHidden":610},[609],[572,990,992,996],{"className":991},[614],[572,993],{"className":994,"style":995},[618],"height:0.6444em;",[572,997,983],{"className":998},[623]," und löst nach der dritten auf.",[563,1001,1002,1003,1031,1032,1087],{},"Fehlt eine Variable (ihr Koeffizient ist ",[572,1004,1006,1019],{"className":1005},[575],[572,1007,1009],{"className":1008},[579],[581,1010,1011],{"xmlns":583},[585,1012,1013,1017],{},[588,1014,1015],{},[598,1016,983],{},[602,1018,983],{"encoding":604},[572,1020,1022],{"className":1021,"ariaHidden":610},[609],[572,1023,1025,1028],{"className":1024},[614],[572,1026],{"className":1027,"style":995},[618],[572,1029,983],{"className":1030},[623],"), ist die Ebene parallel zur entsprechenden Achse. Ist ",[572,1033,1035,1054],{"className":1034},[575],[572,1036,1038],{"className":1037},[579],[581,1039,1040],{"xmlns":583},[585,1041,1042,1051],{},[588,1043,1044,1046,1049],{},[594,1045,927],{},[845,1047,1048],{},"=",[598,1050,983],{},[602,1052,1053],{"encoding":604},"d = 0",[572,1055,1057,1078],{"className":1056,"ariaHidden":610},[609],[572,1058,1060,1063,1066,1071,1075],{"className":1059},[614],[572,1061],{"className":1062,"style":939},[618],[572,1064,927],{"className":1065},[623,627],[572,1067],{"className":1068,"style":1070},[1069],"mspace","margin-right:0.2778em;",[572,1072,1048],{"className":1073},[1074],"mrel",[572,1076],{"className":1077,"style":1070},[1069],[572,1079,1081,1084],{"className":1080},[614],[572,1082],{"className":1083,"style":995},[618],[572,1085,983],{"className":1086},[623],", geht die Ebene durch den Ursprung.",[558,1089,1091],{"id":1090},"beispiele","Beispiele",[563,1093,1094,1095,1198,1199,1342,1343,678,1576,1605],{},"Ebene durch ",[572,1096,1098,1134],{"className":1097},[575],[572,1099,1101],{"className":1100},[579],[581,1102,1103],{"xmlns":583},[585,1104,1105,1131],{},[588,1106,1107,1110,1114,1116,1119,1121,1123,1126,1128],{},[594,1108,1109],{},"P",[845,1111,1113],{"stretchy":1112},"false","(",[598,1115,600],{},[845,1117,1118],{},"∣",[598,1120,768],{},[845,1122,1118],{},[845,1124,1125],{},"−",[598,1127,600],{},[845,1129,1130],{"stretchy":1112},")",[602,1132,1133],{"encoding":604},"P(1 \\mid 3 \\mid -1)",[572,1135,1137,1164,1182],{"className":1136,"ariaHidden":610},[609],[572,1138,1140,1144,1148,1152,1155,1158,1161],{"className":1139},[614],[572,1141],{"className":1142,"style":1143},[618],"height:1em;vertical-align:-0.25em;",[572,1145,1109],{"className":1146,"style":1147},[623,627],"margin-right:0.1389em;",[572,1149,1113],{"className":1150},[1151],"mopen",[572,1153,600],{"className":1154},[623],[572,1156],{"className":1157,"style":1070},[1069],[572,1159,1118],{"className":1160},[1074],[572,1162],{"className":1163,"style":1070},[1069],[572,1165,1167,1170,1173,1176,1179],{"className":1166},[614],[572,1168],{"className":1169,"style":1143},[618],[572,1171,768],{"className":1172},[623],[572,1174],{"className":1175,"style":1070},[1069],[572,1177,1118],{"className":1178},[1074],[572,1180],{"className":1181,"style":1070},[1069],[572,1183,1185,1188,1191,1194],{"className":1184},[614],[572,1186],{"className":1187,"style":1143},[618],[572,1189,1125],{"className":1190},[623],[572,1192,600],{"className":1193},[623],[572,1195,1130],{"className":1196},[1197],"mclose"," mit Normalenvektor ",[572,1200,1202,1245],{"className":1201},[575],[572,1203,1205],{"className":1204},[579],[581,1206,1207],{"xmlns":583},[585,1208,1209,1242],{},[588,1210,1211,1217,1219,1221,1223,1226,1230,1232,1234,1236,1238,1240],{},[839,1212,1213,1215],{"accent":610},[594,1214,843],{},[845,1216,847],{},[845,1218,1048],{},[845,1220,1113],{"stretchy":1112},[598,1222,697],{},[845,1224,1225],{"separator":610},",",[1227,1228,1229],"mtext",{}," ",[845,1231,1125],{},[598,1233,600],{},[845,1235,1225],{"separator":610},[1227,1237,1229],{},[598,1239,697],{},[845,1241,1130],{"stretchy":1112},[602,1243,1244],{"encoding":604},"\\vec{n} = (2,\\ -1,\\ 2)",[572,1246,1248,1298],{"className":1247,"ariaHidden":610},[609],[572,1249,1251,1254,1289,1292,1295],{"className":1250},[614],[572,1252],{"className":1253,"style":860},[618],[572,1255,1257],{"className":1256},[623,864],[572,1258,1260],{"className":1259},[635],[572,1261,1263],{"className":1262},[640],[572,1264,1266,1274],{"className":1265,"style":860},[644],[572,1267,1268,1271],{"style":876},[572,1269],{"className":1270,"style":880},[652],[572,1272,843],{"className":1273},[623,627],[572,1275,1276,1279],{"style":876},[572,1277],{"className":1278,"style":880},[652],[572,1280,1282],{"className":1281,"style":893},[892],[572,1283,1285],{"className":1284,"style":898},[897],[900,1286,1287],{"xmlns":902,"width":903,"height":904,"style":905,"viewBox":906,"preserveAspectRatio":907},[909,1288],{"d":911},[572,1290],{"className":1291,"style":1070},[1069],[572,1293,1048],{"className":1294},[1074],[572,1296],{"className":1297,"style":1070},[1069],[572,1299,1301,1304,1307,1310,1314,1317,1321,1324,1327,1330,1333,1336,1339],{"className":1300},[614],[572,1302],{"className":1303,"style":1143},[618],[572,1305,1113],{"className":1306},[1151],[572,1308,697],{"className":1309},[623],[572,1311,1225],{"className":1312},[1313],"mpunct",[572,1315,1229],{"className":1316},[1069],[572,1318],{"className":1319,"style":1320},[1069],"margin-right:0.1667em;",[572,1322,1125],{"className":1323},[623],[572,1325,600],{"className":1326},[623],[572,1328,1225],{"className":1329},[1313],[572,1331,1229],{"className":1332},[1069],[572,1334],{"className":1335,"style":1320},[1069],[572,1337,697],{"className":1338},[623],[572,1340,1130],{"className":1341},[1197],". Ansatz ",[572,1344,1346,1389],{"className":1345},[575],[572,1347,1349],{"className":1348},[579],[581,1350,1351],{"xmlns":583},[585,1352,1353,1386],{},[588,1354,1355,1357,1363,1365,1371,1374,1376,1382,1384],{},[598,1356,697],{},[591,1358,1359,1361],{},[594,1360,596],{},[598,1362,600],{},[845,1364,1125],{},[591,1366,1367,1369],{},[594,1368,596],{},[598,1370,697],{},[845,1372,1373],{},"+",[598,1375,697],{},[591,1377,1378,1380],{},[594,1379,596],{},[598,1381,768],{},[845,1383,1048],{},[594,1385,927],{},[602,1387,1388],{"encoding":604},"2x_1 - x_2 + 2x_3 = d",[572,1390,1392,1453,1509,1567],{"className":1391,"ariaHidden":610},[609],[572,1393,1395,1399,1402,1442,1446,1450],{"className":1394},[614],[572,1396],{"className":1397,"style":1398},[618],"height:0.7944em;vertical-align:-0.15em;",[572,1400,697],{"className":1401},[623],[572,1403,1405,1408],{"className":1404},[623],[572,1406,596],{"className":1407},[623,627],[572,1409,1411],{"className":1410},[631],[572,1412,1414,1434],{"className":1413},[635,636],[572,1415,1417,1431],{"className":1416},[640],[572,1418,1420],{"className":1419,"style":645},[644],[572,1421,1422,1425],{"style":648},[572,1423],{"className":1424,"style":653},[652],[572,1426,1428],{"className":1427},[657,658,659,660],[572,1429,600],{"className":1430},[623,660],[572,1432,668],{"className":1433},[667],[572,1435,1437],{"className":1436},[640],[572,1438,1440],{"className":1439,"style":675},[644],[572,1441],{},[572,1443],{"className":1444,"style":1445},[1069],"margin-right:0.2222em;",[572,1447,1125],{"className":1448},[1449],"mbin",[572,1451],{"className":1452,"style":1445},[1069],[572,1454,1456,1460,1500,1503,1506],{"className":1455},[614],[572,1457],{"className":1458,"style":1459},[618],"height:0.7333em;vertical-align:-0.15em;",[572,1461,1463,1466],{"className":1462},[623],[572,1464,596],{"className":1465},[623,627],[572,1467,1469],{"className":1468},[631],[572,1470,1472,1492],{"className":1471},[635,636],[572,1473,1475,1489],{"className":1474},[640],[572,1476,1478],{"className":1477,"style":645},[644],[572,1479,1480,1483],{"style":648},[572,1481],{"className":1482,"style":653},[652],[572,1484,1486],{"className":1485},[657,658,659,660],[572,1487,697],{"className":1488},[623,660],[572,1490,668],{"className":1491},[667],[572,1493,1495],{"className":1494},[640],[572,1496,1498],{"className":1497,"style":675},[644],[572,1499],{},[572,1501],{"className":1502,"style":1445},[1069],[572,1504,1373],{"className":1505},[1449],[572,1507],{"className":1508,"style":1445},[1069],[572,1510,1512,1515,1518,1558,1561,1564],{"className":1511},[614],[572,1513],{"className":1514,"style":1398},[618],[572,1516,697],{"className":1517},[623],[572,1519,1521,1524],{"className":1520},[623],[572,1522,596],{"className":1523},[623,627],[572,1525,1527],{"className":1526},[631],[572,1528,1530,1550],{"className":1529},[635,636],[572,1531,1533,1547],{"className":1532},[640],[572,1534,1536],{"className":1535,"style":645},[644],[572,1537,1538,1541],{"style":648},[572,1539],{"className":1540,"style":653},[652],[572,1542,1544],{"className":1543},[657,658,659,660],[572,1545,768],{"className":1546},[623,660],[572,1548,668],{"className":1549},[667],[572,1551,1553],{"className":1552},[640],[572,1554,1556],{"className":1555,"style":675},[644],[572,1557],{},[572,1559],{"className":1560,"style":1070},[1069],[572,1562,1048],{"className":1563},[1074],[572,1565],{"className":1566,"style":1070},[1069],[572,1568,1570,1573],{"className":1569},[614],[572,1571],{"className":1572,"style":939},[618],[572,1574,927],{"className":1575},[623,627],[572,1577,1579,1592],{"className":1578},[575],[572,1580,1582],{"className":1581},[579],[581,1583,1584],{"xmlns":583},[585,1585,1586,1590],{},[588,1587,1588],{},[594,1589,1109],{},[602,1591,1109],{"encoding":604},[572,1593,1595],{"className":1594,"ariaHidden":610},[609],[572,1596,1598,1602],{"className":1597},[614],[572,1599],{"className":1600,"style":1601},[618],"height:0.6833em;",[572,1603,1109],{"className":1604,"style":1147},[623,627]," einsetzen:",[572,1607,1610],{"className":1608},[1609],"katex-display",[572,1611,1613,1722],{"className":1612},[575],[572,1614,1616],{"className":1615},[579],[581,1617,1619],{"xmlns":583,"display":1618},"block",[585,1620,1621,1719],{},[588,1622,1623,1625,1627,1629,1632,1634,1636,1638,1640,1642,1644,1646,1648,1650,1652,1654,1656,1658,1661,1664,1666,1669,1671,1674,1678,1681,1684,1687,1689,1695,1697,1703,1705,1707,1713,1715,1717],{},[594,1624,927],{},[845,1626,1048],{},[598,1628,697],{},[845,1630,1631],{},"⋅",[598,1633,600],{},[845,1635,1125],{},[598,1637,768],{},[845,1639,1373],{},[598,1641,697],{},[845,1643,1631],{},[845,1645,1113],{"stretchy":1112},[845,1647,1125],{},[598,1649,600],{},[845,1651,1130],{"stretchy":1112},[845,1653,1048],{},[845,1655,1125],{},[598,1657,768],{},[1069,1659],{"width":1660},"1em",[845,1662,1663],{},"⇒",[1069,1665],{"width":1660},[594,1667,1668],{},"E",[1069,1670],{},[1069,1672],{"width":1673},"0.1111em",[845,1675],{"lspace":1676,"rspace":1677},"0em","0.17em",[1227,1679,1680],{}," ⁣",[845,1682,1683],{"lspace":1676,"rspace":1676},":",[1069,1685],{"width":1686},"0.3333em",[598,1688,697],{},[591,1690,1691,1693],{},[594,1692,596],{},[598,1694,600],{},[845,1696,1125],{},[591,1698,1699,1701],{},[594,1700,596],{},[598,1702,697],{},[845,1704,1373],{},[598,1706,697],{},[591,1708,1709,1711],{},[594,1710,596],{},[598,1712,768],{},[845,1714,1048],{},[845,1716,1125],{},[598,1718,768],{},[602,1720,1721],{"encoding":604},"d = 2 \\cdot 1 - 3 + 2 \\cdot (-1) = -3\n\\quad\\Rightarrow\\quad\nE\\colon 2x_1 - x_2 + 2x_3 = -3",[572,1723,1725,1743,1761,1780,1798,1816,1843,1871,1962,2017,2075],{"className":1724,"ariaHidden":610},[609],[572,1726,1728,1731,1734,1737,1740],{"className":1727},[614],[572,1729],{"className":1730,"style":939},[618],[572,1732,927],{"className":1733},[623,627],[572,1735],{"className":1736,"style":1070},[1069],[572,1738,1048],{"className":1739},[1074],[572,1741],{"className":1742,"style":1070},[1069],[572,1744,1746,1749,1752,1755,1758],{"className":1745},[614],[572,1747],{"className":1748,"style":995},[618],[572,1750,697],{"className":1751},[623],[572,1753],{"className":1754,"style":1445},[1069],[572,1756,1631],{"className":1757},[1449],[572,1759],{"className":1760,"style":1445},[1069],[572,1762,1764,1768,1771,1774,1777],{"className":1763},[614],[572,1765],{"className":1766,"style":1767},[618],"height:0.7278em;vertical-align:-0.0833em;",[572,1769,600],{"className":1770},[623],[572,1772],{"className":1773,"style":1445},[1069],[572,1775,1125],{"className":1776},[1449],[572,1778],{"className":1779,"style":1445},[1069],[572,1781,1783,1786,1789,1792,1795],{"className":1782},[614],[572,1784],{"className":1785,"style":1767},[618],[572,1787,768],{"className":1788},[623],[572,1790],{"className":1791,"style":1445},[1069],[572,1793,1373],{"className":1794},[1449],[572,1796],{"className":1797,"style":1445},[1069],[572,1799,1801,1804,1807,1810,1813],{"className":1800},[614],[572,1802],{"className":1803,"style":995},[618],[572,1805,697],{"className":1806},[623],[572,1808],{"className":1809,"style":1445},[1069],[572,1811,1631],{"className":1812},[1449],[572,1814],{"className":1815,"style":1445},[1069],[572,1817,1819,1822,1825,1828,1831,1834,1837,1840],{"className":1818},[614],[572,1820],{"className":1821,"style":1143},[618],[572,1823,1113],{"className":1824},[1151],[572,1826,1125],{"className":1827},[623],[572,1829,600],{"className":1830},[623],[572,1832,1130],{"className":1833},[1197],[572,1835],{"className":1836,"style":1070},[1069],[572,1838,1048],{"className":1839},[1074],[572,1841],{"className":1842,"style":1070},[1069],[572,1844,1846,1849,1852,1855,1859,1862,1865,1868],{"className":1845},[614],[572,1847],{"className":1848,"style":1767},[618],[572,1850,1125],{"className":1851},[623],[572,1853,768],{"className":1854},[623],[572,1856],{"className":1857,"style":1858},[1069],"margin-right:1em;",[572,1860],{"className":1861,"style":1070},[1069],[572,1863,1663],{"className":1864},[1074],[572,1866],{"className":1867,"style":1858},[1069],[572,1869],{"className":1870,"style":1070},[1069],[572,1872,1874,1878,1882,1886,1890,1893,1897,1900,1906,1910,1913,1953,1956,1959],{"className":1873},[614],[572,1875],{"className":1876,"style":1877},[618],"height:0.8333em;vertical-align:-0.15em;",[572,1879,1668],{"className":1880,"style":1881},[623,627],"margin-right:0.0576em;",[572,1883],{"className":1884},[1069,1885],"nobreak",[572,1887],{"className":1888,"style":1889},[1069],"margin-right:0.1111em;",[572,1891],{"className":1892},[1313],[572,1894],{"className":1895,"style":1896},[1069],"margin-right:-0.1667em;",[572,1898],{"className":1899,"style":1320},[1069],[572,1901,1903],{"className":1902},[623],[572,1904,1683],{"className":1905},[1074],[572,1907],{"className":1908,"style":1909},[1069],"margin-right:0.3333em;",[572,1911,697],{"className":1912},[623],[572,1914,1916,1919],{"className":1915},[623],[572,1917,596],{"className":1918},[623,627],[572,1920,1922],{"className":1921},[631],[572,1923,1925,1945],{"className":1924},[635,636],[572,1926,1928,1942],{"className":1927},[640],[572,1929,1931],{"className":1930,"style":645},[644],[572,1932,1933,1936],{"style":648},[572,1934],{"className":1935,"style":653},[652],[572,1937,1939],{"className":1938},[657,658,659,660],[572,1940,600],{"className":1941},[623,660],[572,1943,668],{"className":1944},[667],[572,1946,1948],{"className":1947},[640],[572,1949,1951],{"className":1950,"style":675},[644],[572,1952],{},[572,1954],{"className":1955,"style":1445},[1069],[572,1957,1125],{"className":1958},[1449],[572,1960],{"className":1961,"style":1445},[1069],[572,1963,1965,1968,2008,2011,2014],{"className":1964},[614],[572,1966],{"className":1967,"style":1459},[618],[572,1969,1971,1974],{"className":1970},[623],[572,1972,596],{"className":1973},[623,627],[572,1975,1977],{"className":1976},[631],[572,1978,1980,2000],{"className":1979},[635,636],[572,1981,1983,1997],{"className":1982},[640],[572,1984,1986],{"className":1985,"style":645},[644],[572,1987,1988,1991],{"style":648},[572,1989],{"className":1990,"style":653},[652],[572,1992,1994],{"className":1993},[657,658,659,660],[572,1995,697],{"className":1996},[623,660],[572,1998,668],{"className":1999},[667],[572,2001,2003],{"className":2002},[640],[572,2004,2006],{"className":2005,"style":675},[644],[572,2007],{},[572,2009],{"className":2010,"style":1445},[1069],[572,2012,1373],{"className":2013},[1449],[572,2015],{"className":2016,"style":1445},[1069],[572,2018,2020,2023,2026,2066,2069,2072],{"className":2019},[614],[572,2021],{"className":2022,"style":1398},[618],[572,2024,697],{"className":2025},[623],[572,2027,2029,2032],{"className":2028},[623],[572,2030,596],{"className":2031},[623,627],[572,2033,2035],{"className":2034},[631],[572,2036,2038,2058],{"className":2037},[635,636],[572,2039,2041,2055],{"className":2040},[640],[572,2042,2044],{"className":2043,"style":645},[644],[572,2045,2046,2049],{"style":648},[572,2047],{"className":2048,"style":653},[652],[572,2050,2052],{"className":2051},[657,658,659,660],[572,2053,768],{"className":2054},[623,660],[572,2056,668],{"className":2057},[667],[572,2059,2061],{"className":2060},[640],[572,2062,2064],{"className":2063,"style":675},[644],[572,2065],{},[572,2067],{"className":2068,"style":1070},[1069],[572,2070,1048],{"className":2071},[1074],[572,2073],{"className":2074,"style":1070},[1069],[572,2076,2078,2081,2084],{"className":2077},[614],[572,2079],{"className":2080,"style":1767},[618],[572,2082,1125],{"className":2083},[623],[572,2085,768],{"className":2086},[623],[563,2088,2089,2090,2184,2185,678,2285,2314,2315,2343,2344,2184,2434,678,2598,2626,2627,2655],{},"Punktprobe: ",[572,2091,2093,2124],{"className":2092},[575],[572,2094,2096],{"className":2095},[579],[581,2097,2098],{"xmlns":583},[585,2099,2100,2121],{},[588,2101,2102,2105,2107,2109,2111,2113,2115,2117,2119],{},[594,2103,2104],{},"Q",[845,2106,1113],{"stretchy":1112},[598,2108,983],{},[845,2110,1118],{},[598,2112,600],{},[845,2114,1118],{},[845,2116,1125],{},[598,2118,600],{},[845,2120,1130],{"stretchy":1112},[602,2122,2123],{"encoding":604},"Q(0 \\mid 1 \\mid -1)",[572,2125,2127,2151,2169],{"className":2126,"ariaHidden":610},[609],[572,2128,2130,2133,2136,2139,2142,2145,2148],{"className":2129},[614],[572,2131],{"className":2132,"style":1143},[618],[572,2134,2104],{"className":2135},[623,627],[572,2137,1113],{"className":2138},[1151],[572,2140,983],{"className":2141},[623],[572,2143],{"className":2144,"style":1070},[1069],[572,2146,1118],{"className":2147},[1074],[572,2149],{"className":2150,"style":1070},[1069],[572,2152,2154,2157,2160,2163,2166],{"className":2153},[614],[572,2155],{"className":2156,"style":1143},[618],[572,2158,600],{"className":2159},[623],[572,2161],{"className":2162,"style":1070},[1069],[572,2164,1118],{"className":2165},[1074],[572,2167],{"className":2168,"style":1070},[1069],[572,2170,2172,2175,2178,2181],{"className":2171},[614],[572,2173],{"className":2174,"style":1143},[618],[572,2176,1125],{"className":2177},[623],[572,2179,600],{"className":2180},[623],[572,2182,1130],{"className":2183},[1197]," liefert ",[572,2186,2188,2216],{"className":2187},[575],[572,2189,2191],{"className":2190},[579],[581,2192,2193],{"xmlns":583},[585,2194,2195,2213],{},[588,2196,2197,2199,2201,2203,2205,2207,2209,2211],{},[598,2198,983],{},[845,2200,1125],{},[598,2202,600],{},[845,2204,1125],{},[598,2206,697],{},[845,2208,1048],{},[845,2210,1125],{},[598,2212,768],{},[602,2214,2215],{"encoding":604},"0 - 1 - 2 = -3",[572,2217,2219,2237,2255,2273],{"className":2218,"ariaHidden":610},[609],[572,2220,2222,2225,2228,2231,2234],{"className":2221},[614],[572,2223],{"className":2224,"style":1767},[618],[572,2226,983],{"className":2227},[623],[572,2229],{"className":2230,"style":1445},[1069],[572,2232,1125],{"className":2233},[1449],[572,2235],{"className":2236,"style":1445},[1069],[572,2238,2240,2243,2246,2249,2252],{"className":2239},[614],[572,2241],{"className":2242,"style":1767},[618],[572,2244,600],{"className":2245},[623],[572,2247],{"className":2248,"style":1445},[1069],[572,2250,1125],{"className":2251},[1449],[572,2253],{"className":2254,"style":1445},[1069],[572,2256,2258,2261,2264,2267,2270],{"className":2257},[614],[572,2259],{"className":2260,"style":995},[618],[572,2262,697],{"className":2263},[623],[572,2265],{"className":2266,"style":1070},[1069],[572,2268,1048],{"className":2269},[1074],[572,2271],{"className":2272,"style":1070},[1069],[572,2274,2276,2279,2282],{"className":2275},[614],[572,2277],{"className":2278,"style":1767},[618],[572,2280,1125],{"className":2281},[623],[572,2283,768],{"className":2284},[623],[572,2286,2288,2301],{"className":2287},[575],[572,2289,2291],{"className":2290},[579],[581,2292,2293],{"xmlns":583},[585,2294,2295,2299],{},[588,2296,2297],{},[594,2298,2104],{},[602,2300,2104],{"encoding":604},[572,2302,2304],{"className":2303,"ariaHidden":610},[609],[572,2305,2307,2311],{"className":2306},[614],[572,2308],{"className":2309,"style":2310},[618],"height:0.8778em;vertical-align:-0.1944em;",[572,2312,2104],{"className":2313},[623,627]," liegt in ",[572,2316,2318,2331],{"className":2317},[575],[572,2319,2321],{"className":2320},[579],[581,2322,2323],{"xmlns":583},[585,2324,2325,2329],{},[588,2326,2327],{},[594,2328,1668],{},[602,2330,1668],{"encoding":604},[572,2332,2334],{"className":2333,"ariaHidden":610},[609],[572,2335,2337,2340],{"className":2336},[614],[572,2338],{"className":2339,"style":1601},[618],[572,2341,1668],{"className":2342,"style":1881},[623,627],". ",[572,2345,2347,2376],{"className":2346},[575],[572,2348,2350],{"className":2349},[579],[581,2351,2352],{"xmlns":583},[585,2353,2354,2373],{},[588,2355,2356,2359,2361,2363,2365,2367,2369,2371],{},[594,2357,2358],{},"R",[845,2360,1113],{"stretchy":1112},[598,2362,600],{},[845,2364,1118],{},[598,2366,600],{},[845,2368,1118],{},[598,2370,600],{},[845,2372,1130],{"stretchy":1112},[602,2374,2375],{"encoding":604},"R(1 \\mid 1 \\mid 1)",[572,2377,2379,2404,2422],{"className":2378,"ariaHidden":610},[609],[572,2380,2382,2385,2389,2392,2395,2398,2401],{"className":2381},[614],[572,2383],{"className":2384,"style":1143},[618],[572,2386,2358],{"className":2387,"style":2388},[623,627],"margin-right:0.0077em;",[572,2390,1113],{"className":2391},[1151],[572,2393,600],{"className":2394},[623],[572,2396],{"className":2397,"style":1070},[1069],[572,2399,1118],{"className":2400},[1074],[572,2402],{"className":2403,"style":1070},[1069],[572,2405,2407,2410,2413,2416,2419],{"className":2406},[614],[572,2408],{"className":2409,"style":1143},[618],[572,2411,600],{"className":2412},[623],[572,2414],{"className":2415,"style":1070},[1069],[572,2417,1118],{"className":2418},[1074],[572,2420],{"className":2421,"style":1070},[1069],[572,2423,2425,2428,2431],{"className":2424},[614],[572,2426],{"className":2427,"style":1143},[618],[572,2429,600],{"className":2430},[623],[572,2432,1130],{"className":2433},[1197],[572,2435,2437,2471],{"className":2436},[575],[572,2438,2440],{"className":2439},[579],[581,2441,2442],{"xmlns":583},[585,2443,2444,2468],{},[588,2445,2446,2448,2450,2452,2454,2456,2458,2460,2464,2466],{},[598,2447,697],{},[845,2449,1125],{},[598,2451,600],{},[845,2453,1373],{},[598,2455,697],{},[845,2457,1048],{},[598,2459,768],{},[845,2461,2463],{"mathvariant":2462},"normal","≠",[845,2465,1125],{},[598,2467,768],{},[602,2469,2470],{"encoding":604},"2 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liegt nicht in ",[572,2628,2630,2643],{"className":2629},[575],[572,2631,2633],{"className":2632},[579],[581,2634,2635],{"xmlns":583},[585,2636,2637,2641],{},[588,2638,2639],{},[594,2640,1668],{},[602,2642,1668],{"encoding":604},[572,2644,2646],{"className":2645,"ariaHidden":610},[609],[572,2647,2649,2652],{"className":2648},[614],[572,2650],{"className":2651,"style":1601},[618],[572,2653,1668],{"className":2654,"style":1881},[623,627],".",[563,2657,2658,2659,1683],{},"Spurpunkte der Ebene ",[572,2660,2662,2709],{"className":2661},[575],[572,2663,2665],{"className":2664},[579],[581,2666,2667],{"xmlns":583},[585,2668,2669,2706],{},[588,2670,2671,2673,2679,2681,2684,2690,2692,2695,2701,2703],{},[598,2672,768],{},[591,2674,2675,2677],{},[594,2676,596],{},[598,2678,600],{},[845,2680,1125],{},[598,2682,2683],{},"6",[591,2685,2686,2688],{},[594,2687,596],{},[598,2689,697],{},[845,2691,1373],{},[598,2693,2694],{},"5",[591,2696,2697,2699],{},[594,2698,596],{},[598,2700,768],{},[845,2702,1048],{},[598,2704,2705],{},"13",[602,2707,2708],{"encoding":604},"3x_1 - 6x_2 + 5x_3 = 13",[572,2710,2712,2770,2828,2886],{"className":2711,"ariaHidden":610},[609],[572,2713,2715,2718,2721,2761,2764,2767],{"className":2714},[614],[572,2716],{"className":2717,"style":1398},[618],[572,2719,768],{"className":2720},[623],[572,2722,2724,2727],{"className":2723},[623],[572,2725,596],{"className":2726},[623,627],[572,2728,2730],{"className":2729},[631],[572,2731,2733,2753],{"className":2732},[635,636],[572,2734,2736,2750],{"className":2735},[640],[572,2737,2739],{"className":2738,"style":645},[644],[572,2740,2741,2744],{"style":648},[572,2742],{"className":2743,"style":653},[652],[572,2745,2747],{"className":2746},[657,658,659,660],[572,2748,600],{"className":2749},[623,660],[572,2751,668],{"className":2752},[667],[572,2754,2756],{"className":2755},[640],[572,2757,2759],{"className":2758,"style":675},[644],[572,2760],{},[572,2762],{"className":2763,"style":1445},[1069],[572,2765,1125],{"className":2766},[1449],[572,2768],{"className":2769,"style":1445},[1069],[572,2771,2773,2776,2779,2819,2822,2825],{"className":2772},[614],[572,2774],{"className":2775,"style":1398},[618],[572,2777,2683],{"className":2778},[623],[572,2780,2782,2785],{"className":2781},[623],[572,2783,596],{"className":2784},[623,627],[572,2786,2788],{"className":2787},[631],[572,2789,2791,2811],{"className":2790},[635,636],[572,2792,2794,2808],{"className":2793},[640],[572,2795,2797],{"className":2796,"style":645},[644],[572,2798,2799,2802],{"style":648},[572,2800],{"className":2801,"style":653},[652],[572,2803,2805],{"className":2804},[657,658,659,660],[572,2806,697],{"className":2807},[623,660],[572,2809,668],{"className":2810},[667],[572,2812,2814],{"className":2813},[640],[572,2815,2817],{"className":2816,"style":675},[644],[572,2818],{},[572,2820],{"className":2821,"style":1445},[1069],[572,2823,1373],{"className":2824},[1449],[572,2826],{"className":2827,"style":1445},[1069],[572,2829,2831,2834,2837,2877,2880,2883],{"className":2830},[614],[572,2832],{"className":2833,"style":1398},[618],[572,2835,2694],{"className":2836},[623],[572,2838,2840,2843],{"className":2839},[623],[572,2841,596],{"className":2842},[623,627],[572,2844,2846],{"className":2845},[631],[572,2847,2849,2869],{"className":2848},[635,636],[572,2850,2852,2866],{"className":2851},[640],[572,2853,2855],{"className":2854,"style":645},[644],[572,2856,2857,2860],{"style":648},[572,2858],{"className":2859,"style":653},[652],[572,2861,2863],{"className":2862},[657,658,659,660],[572,2864,768],{"className":2865},[623,660],[572,2867,668],{"className":2868},[667],[572,2870,2872],{"className":2871},[640],[572,2873,2875],{"className":2874,"style":675},[644],[572,2876],{},[572,2878],{"className":2879,"style":1070},[1069],[572,2881,1048],{"className":2882},[1074],[572,2884],{"className":2885,"style":1070},[1069],[572,2887,2889,2892],{"className":2888},[614],[572,2890],{"className":2891,"style":995},[618],[572,2893,2705],{"className":2894},[623],[572,2896,2898],{"className":2897},[1609],[572,2899,2901,3010],{"className":2900},[575],[572,2902,2904],{"className":2903},[579],[581,2905,2906],{"xmlns":583,"display":1618},[585,2907,2908,3007],{},[588,2909,2910,2917,2941,2943,2945,2951,2975,2977,2979,2985],{},[591,2911,2912,2915],{},[594,2913,2914],{},"S",[598,2916,600],{},[588,2918,2919,2921,2931,2933,2935,2937,2939],{},[845,2920,1113],{"fence":610},[2922,2923,2924],"mstyle",{"scriptlevel":983,"displaystyle":1112},[2925,2926,2927,2929],"mfrac",{},[598,2928,2705],{},[598,2930,768],{},[845,2932,1118],{},[598,2934,983],{},[845,2936,1118],{},[598,2938,983],{},[845,2940,1130],{"fence":610},[845,2942,1225],{"separator":610},[1069,2944],{"width":1660},[591,2946,2947,2949],{},[594,2948,2914],{},[598,2950,697],{},[588,2952,2953,2955,2957,2959,2961,2969,2971,2973],{},[845,2954,1113],{"fence":610},[598,2956,983],{},[845,2958,1118],{},[845,2960,1125],{},[2922,2962,2963],{"scriptlevel":983,"displaystyle":1112},[2925,2964,2965,2967],{},[598,2966,2705],{},[598,2968,2683],{},[845,2970,1118],{},[598,2972,983],{},[845,2974,1130],{"fence":610},[845,2976,1225],{"separator":610},[1069,2978],{"width":1660},[591,2980,2981,2983],{},[594,2982,2914],{},[598,2984,768],{},[588,2986,2987,2989,2991,2993,2995,2997,3005],{},[845,2988,1113],{"fence":610},[598,2990,983],{},[845,2992,1118],{},[598,2994,983],{},[845,2996,1118],{},[2922,2998,2999],{"scriptlevel":983,"displaystyle":1112},[2925,3000,3001,3003],{},[598,3002,2705],{},[598,3004,2694],{},[845,3006,1130],{"fence":610},[602,3008,3009],{"encoding":604},"S_1\\left(\\tfrac{13}{3} \\mid 0 \\mid 0\\right), \\quad S_2\\left(0 \\mid -\\tfrac{13}{6} \\mid 0\\right), \\quad S_3\\left(0 \\mid 0 \\mid \\tfrac{13}{5}\\right)",[572,3011,3013],{"className":3012,"ariaHidden":610},[609],[572,3014,3016,3020,3061,3064,3184,3187,3190,3193,3196,3236,3239,3349,3352,3355,3358,3361,3401,3404],{"className":3015},[614],[572,3017],{"className":3018,"style":3019},[618],"height:1.2em;vertical-align:-0.35em;",[572,3021,3023,3026],{"className":3022},[623],[572,3024,2914],{"className":3025,"style":1881},[623,627],[572,3027,3029],{"className":3028},[631],[572,3030,3032,3053],{"className":3031},[635,636],[572,3033,3035,3050],{"className":3034},[640],[572,3036,3038],{"className":3037,"style":645},[644],[572,3039,3041,3044],{"style":3040},"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;",[572,3042],{"className":3043,"style":653},[652],[572,3045,3047],{"className":3046},[657,658,659,660],[572,3048,600],{"className":3049},[623,660],[572,3051,668],{"className":3052},[667],[572,3054,3056],{"className":3055},[640],[572,3057,3059],{"className":3058,"style":675},[644],[572,3060],{},[572,3062],{"className":3063,"style":1320},[1069],[572,3065,3068,3078,3154,3157,3160,3163,3166,3169,3172,3175,3178],{"className":3066},[3067],"minner",[572,3069,3073],{"className":3070,"style":3072},[1151,3071],"delimcenter","top:0em;",[572,3074,1113],{"className":3075},[3076,3077],"delimsizing","size1",[572,3079,3081,3085,3151],{"className":3080},[623],[572,3082],{"className":3083},[1151,3084],"nulldelimiter",[572,3086,3088],{"className":3087},[2925],[572,3089,3091,3142],{"className":3090},[635,636],[572,3092,3094,3139],{"className":3093},[640],[572,3095,3098,3113,3124],{"className":3096,"style":3097},[644],"height:0.8451em;",[572,3099,3101,3104],{"style":3100},"top:-2.655em;",[572,3102],{"className":3103,"style":880},[652],[572,3105,3107],{"className":3106},[657,658,659,660],[572,3108,3110],{"className":3109},[623,660],[572,3111,768],{"className":3112},[623,660],[572,3114,3116,3119],{"style":3115},"top:-3.23em;",[572,3117],{"className":3118,"style":880},[652],[572,3120],{"className":3121,"style":3123},[3122],"frac-line","border-bottom-width:0.04em;",[572,3125,3127,3130],{"style":3126},"top:-3.394em;",[572,3128],{"className":3129,"style":880},[652],[572,3131,3133],{"className":3132},[657,658,659,660],[572,3134,3136],{"className":3135},[623,660],[572,3137,2705],{"className":3138},[623,660],[572,3140,668],{"className":3141},[667],[572,3143,3145],{"className":3144},[640],[572,3146,3149],{"className":3147,"style":3148},[644],"height:0.345em;",[572,3150],{},[572,3152],{"className":3153},[1197,3084],[572,3155],{"className":3156,"style":1070},[1069],[572,3158,1118],{"className":3159},[1074],[572,3161],{"className":3162,"style":1070},[1069],[572,3164,983],{"className":3165},[623],[572,3167],{"className":3168,"style":1070},[1069],[572,3170,1118],{"className":3171},[1074],[572,3173],{"className":3174,"style":1070},[1069],[572,3176,983],{"className":3177},[623],[572,3179,3181],{"className":3180,"style":3072},[1197,3071],[572,3182,1130],{"className":3183},[3076,3077],[572,3185],{"className":3186,"style":1320},[1069],[572,3188,1225],{"className":3189},[1313],[572,3191],{"className":3192,"style":1858},[1069],[572,3194],{"className":3195,"style":1320},[1069],[572,3197,3199,3202],{"className":3198},[623],[572,3200,2914],{"className":3201,"style":1881},[623,627],[572,3203,3205],{"className":3204},[631],[572,3206,3208,3228],{"className":3207},[635,636],[572,3209,3211,3225],{"className":3210},[640],[572,3212,3214],{"className":3213,"style":645},[644],[572,3215,3216,3219],{"style":3040},[572,3217],{"className":3218,"style":653},[652],[572,3220,3222],{"className":3221},[657,658,659,660],[572,3223,697],{"className":3224},[623,660],[572,3226,668],{"className":3227},[667],[572,3229,3231],{"className":3230},[640],[572,3232,3234],{"className":3233,"style":675},[644],[572,3235],{},[572,3237],{"className":3238,"style":1320},[1069],[572,3240,3242,3248,3251,3254,3257,3260,3263,3331,3334,3337,3340,3343],{"className":3241},[3067],[572,3243,3245],{"className":3244,"style":3072},[1151,3071],[572,3246,1113],{"className":3247},[3076,3077],[572,3249,983],{"className":3250},[623],[572,3252],{"className":3253,"style":1070},[1069],[572,3255,1118],{"className":3256},[1074],[572,3258],{"className":3259,"style":1070},[1069],[572,3261,1125],{"className":3262},[623],[572,3264,3266,3269,3328],{"className":3265},[623],[572,3267],{"className":3268},[1151,3084],[572,3270,3272],{"className":3271},[2925],[572,3273,3275,3320],{"className":3274},[635,636],[572,3276,3278,3317],{"className":3277},[640],[572,3279,3281,3295,3303],{"className":3280,"style":3097},[644],[572,3282,3283,3286],{"style":3100},[572,3284],{"className":3285,"style":880},[652],[572,3287,3289],{"className":3288},[657,658,659,660],[572,3290,3292],{"className":3291},[623,660],[572,3293,2683],{"className":3294},[623,660],[572,3296,3297,3300],{"style":3115},[572,3298],{"className":3299,"style":880},[652],[572,3301],{"className":3302,"style":3123},[3122],[572,3304,3305,3308],{"style":3126},[572,3306],{"className":3307,"style":880},[652],[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Ebene ist dieselbe wie in der Normalenform mit ",[572,3515,3517,3557],{"className":3516},[575],[572,3518,3520],{"className":3519},[579],[581,3521,3522],{"xmlns":583},[585,3523,3524,3554],{},[588,3525,3526,3532,3534,3536,3538,3540,3542,3544,3546,3548,3550,3552],{},[839,3527,3528,3530],{"accent":610},[594,3529,843],{},[845,3531,847],{},[845,3533,1048],{},[845,3535,1113],{"stretchy":1112},[598,3537,768],{},[845,3539,1225],{"separator":610},[1227,3541,1229],{},[845,3543,1125],{},[598,3545,2683],{},[845,3547,1225],{"separator":610},[1227,3549,1229],{},[598,3551,2694],{},[845,3553,1130],{"stretchy":1112},[602,3555,3556],{"encoding":604},"\\vec{n} = (3,\\ -6,\\ 5)",[572,3558,3560,3610],{"className":3559,"ariaHidden":610},[609],[572,3561,3563,3566,3601,3604,3607],{"className":3562},[614],[572,3564],{"className":3565,"style":860},[618],[572,3567,3569],{"className":3568},[623,864],[572,3570,3572],{"className":3571},[635],[572,3573,3575],{"className":3574},[640],[572,3576,3578,3586],{"className":3577,"style":860},[644],[572,3579,3580,3583],{"style":876},[572,3581],{"className":3582,"style":880},[652],[572,3584,843],{"className":3585},[623,627],[572,3587,3588,3591],{"style":876},[572,3589],{"className":3590,"style":880},[652],[572,3592,3594],{"className":3593,"style":893},[892],[572,3595,3597],{"className":3596,"style":898},[897],[900,3598,3599],{"xmlns":902,"width":903,"height":904,"style":905,"viewBox":906,"preserveAspectRatio":907},[909,3600],{"d":911},[572,3602],{"className":3603,"style":1070},[1069],[572,3605,1048],{"className":3606},[1074],[572,3608],{"className":3609,"style":1070},[1069],[572,3611,3613,3616,3619,3622,3625,3628,3631,3634,3637,3640,3643,3646,3649],{"className":3612},[614],[572,3614],{"className":3615,"style":1143},[618],[572,3617,1113],{"className":3618},[1151],[572,3620,768],{"className":3621},[623],[572,3623,1225],{"className":3624},[1313],[572,3626,1229],{"className":3627},[1069],[572,3629],{"className":3630,"style":1320},[1069],[572,3632,1125],{"className":3633},[623],[572,3635,2683],{"className":3636},[623],[572,3638,1225],{"className":3639},[1313],[572,3641,1229],{"className":3642},[1069],[572,3644],{"className":3645,"style":1320},[1069],[572,3647,2694],{"className":3648},[623],[572,3650,1130],{"className":3651},[1197]," durch ",[572,3654,3656,3684],{"className":3655},[575],[572,3657,3659],{"className":3658},[579],[581,3660,3661],{"xmlns":583},[585,3662,3663,3681],{},[588,3664,3665,3667,3669,3671,3673,3675,3677,3679],{},[594,3666,1109],{},[845,3668,1113],{"stretchy":1112},[598,3670,600],{},[845,3672,1118],{},[598,3674,983],{},[845,3676,1118],{},[598,3678,697],{},[845,3680,1130],{"stretchy":1112},[602,3682,3683],{"encoding":604},"P(1 \\mid 0 \\mid 2)",[572,3685,3687,3711,3729],{"className":3686,"ariaHidden":610},[609],[572,3688,3690,3693,3696,3699,3702,3705,3708],{"className":3689},[614],[572,3691],{"className":3692,"style":1143},[618],[572,3694,1109],{"className":3695,"style":1147},[623,627],[572,3697,1113],{"className":3698},[1151],[572,3700,600],{"className":3701},[623],[572,3703],{"className":3704,"style":1070},[1069],[572,3706,1118],{"className":3707},[1074],[572,3709],{"className":3710,"style":1070},[1069],[572,3712,3714,3717,3720,3723,3726],{"className":3713},[614],[572,3715],{"className":3716,"style":1143},[618],[572,3718,983],{"className":3719},[623],[572,3721],{"className":3722,"style":1070},[1069],[572,3724,1118],{"className":3725},[1074],[572,3727],{"className":3728,"style":1070},[1069],[572,3730,3732,3735,3738],{"className":3731},[614],[572,3733],{"className":3734,"style":1143},[618],[572,3736,697],{"className":3737},[623],[572,3739,1130],{"className":3740},[1197],": ",[572,3743,3745,3779],{"className":3744},[575],[572,3746,3748],{"className":3747},[579],[581,3749,3750],{"xmlns":583},[585,3751,3752,3776],{},[588,3753,3754,3756,3758,3760,3762,3764,3766,3768,3770,3772,3774],{},[598,3755,768],{},[845,3757,1631],{},[598,3759,600],{},[845,3761,1125],{},[598,3763,983],{},[845,3765,1373],{},[598,3767,2694],{},[845,3769,1631],{},[598,3771,697],{},[845,3773,1048],{},[598,3775,2705],{},[602,3777,3778],{"encoding":604},"3 \\cdot 1 - 0 + 5 \\cdot 2 = 13",[572,3780,3782,3800,3818,3836,3854,3872],{"className":3781,"ariaHidden":610},[609],[572,3783,3785,3788,3791,3794,3797],{"className":3784},[614],[572,3786],{"className":3787,"style":995},[618],[572,3789,768],{"className":3790},[623],[572,3792],{"className":3793,"style":1445},[1069],[572,3795,1631],{"className":3796},[1449],[572,3798],{"className":3799,"style":1445},[1069],[572,3801,3803,3806,3809,3812,3815],{"className":3802},[614],[572,3804],{"className":3805,"style":1767},[618],[572,3807,600],{"className":3808},[623],[572,3810],{"className":3811,"style":1445},[1069],[572,3813,1125],{"className":3814},[1449],[572,3816],{"className":3817,"style":1445},[1069],[572,3819,3821,3824,3827,3830,3833],{"className":3820},[614],[572,3822],{"className":3823,"style":1767},[618],[572,3825,983],{"className":3826},[623],[572,3828],{"className":3829,"style":1445},[1069],[572,3831,1373],{"className":3832},[1449],[572,3834],{"className":3835,"style":1445},[1069],[572,3837,3839,3842,3845,3848,3851],{"className":3838},[614],[572,3840],{"className":3841,"style":995},[618],[572,3843,2694],{"className":3844},[623],[572,3846],{"className":3847,"style":1445},[1069],[572,3849,1631],{"className":3850},[1449],[572,3852],{"className":3853,"style":1445},[1069],[572,3855,3857,3860,3863,3866,3869],{"className":3856},[614],[572,3858],{"className":3859,"style":995},[618],[572,3861,697],{"className":3862},[623],[572,3864],{"className":3865,"style":1070},[1069],[572,3867,1048],{"className":3868},[1074],[572,3870],{"className":3871,"style":1070},[1069],[572,3873,3875,3878],{"className":3874},[614],[572,3876],{"className":3877,"style":995},[618],[572,3879,2705],{"className":3880},[623],[558,3882,3884],{"id":3883},"typische-fehler","Typische Fehler",[948,3886,3887,4403,4710],{},[951,3888,3889,3890,3918,3919,4169,4170,2655],{},"Die Konstante ",[572,3891,3893,3906],{"className":3892},[575],[572,3894,3896],{"className":3895},[579],[581,3897,3898],{"xmlns":583},[585,3899,3900,3904],{},[588,3901,3902],{},[594,3903,927],{},[602,3905,927],{"encoding":604},[572,3907,3909],{"className":3908,"ariaHidden":610},[609],[572,3910,3912,3915],{"className":3911},[614],[572,3913],{"className":3914,"style":939},[618],[572,3916,927],{"className":3917},[623,627]," mit falschem Vorzeichen übernehmen. Aus ",[572,3920,3922,3968],{"className":3921},[575],[572,3923,3925],{"className":3924},[579],[581,3926,3927],{"xmlns":583},[585,3928,3929,3965],{},[588,3930,3931,3933,3939,3941,3947,3949,3951,3957,3959,3961,3963],{},[598,3932,697],{},[591,3934,3935,3937],{},[594,3936,596],{},[598,3938,600],{},[845,3940,1125],{},[591,3942,3943,3945],{},[594,3944,596],{},[598,3946,697],{},[845,3948,1373],{},[598,3950,697],{},[591,3952,3953,3955],{},[594,3954,596],{},[598,3956,768],{},[845,3958,1373],{},[598,3960,768],{},[845,3962,1048],{},[598,3964,983],{},[602,3966,3967],{"encoding":604},"2x_1 - x_2 + 2x_3 + 3 = 0",[572,3969,3971,4029,4084,4142,4160],{"className":3970,"ariaHidden":610},[609],[572,3972,3974,3977,3980,4020,4023,4026],{"className":3973},[614],[572,3975],{"className":3976,"style":1398},[618],[572,3978,697],{"className":3979},[623],[572,3981,3983,3986],{"className":3982},[623],[572,3984,596],{"className":3985},[623,627],[572,3987,3989],{"className":3988},[631],[572,3990,3992,4012],{"className":3991},[635,636],[572,3993,3995,4009],{"className":3994},[640],[572,3996,3998],{"className":3997,"style":645},[644],[572,3999,4000,4003],{"style":648},[572,4001],{"className":4002,"style":653},[652],[572,4004,4006],{"className":4005},[657,658,659,660],[572,4007,600],{"className":4008},[623,660],[572,4010,668],{"className":4011},[667],[572,4013,4015],{"className":4014},[640],[572,4016,4018],{"className":4017,"style":675},[644],[572,4019],{},[572,4021],{"className":4022,"style":1445},[1069],[572,4024,1125],{"className":4025},[1449],[572,4027],{"className":4028,"style":1445},[1069],[572,4030,4032,4035,4075,4078,4081],{"className":4031},[614],[572,4033],{"className":4034,"style":1459},[618],[572,4036,4038,4041],{"className":4037},[623],[572,4039,596],{"className":4040},[623,627],[572,4042,4044],{"className":4043},[631],[572,4045,4047,4067],{"className":4046},[635,636],[572,4048,4050,4064],{"className":4049},[640],[572,4051,4053],{"className":4052,"style":645},[644],[572,4054,4055,4058],{"style":648},[572,4056],{"className":4057,"style":653},[652],[572,4059,4061],{"className":4060},[657,658,659,660],[572,4062,697],{"className":4063},[623,660],[572,4065,668],{"className":4066},[667],[572,4068,4070],{"className":4069},[640],[572,4071,4073],{"className":4072,"style":675},[644],[572,4074],{},[572,4076],{"className":4077,"style":1445},[1069],[572,4079,1373],{"className":4080},[1449],[572,4082],{"className":4083,"style":1445},[1069],[572,4085,4087,4090,4093,4133,4136,4139],{"className":4086},[614],[572,4088],{"className":4089,"style":1398},[618],[572,4091,697],{"className":4092},[623],[572,4094,4096,4099],{"className":4095},[623],[572,4097,596],{"className":4098},[623,627],[572,4100,4102],{"className":4101},[631],[572,4103,4105,4125],{"className":4104},[635,636],[572,4106,4108,4122],{"className":4107},[640],[572,4109,4111],{"className":4110,"style":645},[644],[572,4112,4113,4116],{"style":648},[572,4114],{"className":4115,"style":653},[652],[572,4117,4119],{"className":4118},[657,658,659,660],[572,4120,768],{"className":4121},[623,660],[572,4123,668],{"className":4124},[667],[572,4126,4128],{"className":4127},[640],[572,4129,4131],{"className":4130,"style":675},[644],[572,4132],{},[572,4134],{"className":4135,"style":1445},[1069],[572,4137,1373],{"className":4138},[1449],[572,4140],{"className":4141,"style":1445},[1069],[572,4143,4145,4148,4151,4154,4157],{"className":4144},[614],[572,4146],{"className":4147,"style":995},[618],[572,4149,768],{"className":4150},[623],[572,4152],{"className":4153,"style":1070},[1069],[572,4155,1048],{"className":4156},[1074],[572,4158],{"className":4159,"style":1070},[1069],[572,4161,4163,4166],{"className":4162},[614],[572,4164],{"className":4165,"style":995},[618],[572,4167,983],{"className":4168},[623]," wird ",[572,4171,4173,4217],{"className":4172},[575],[572,4174,4176],{"className":4175},[579],[581,4177,4178],{"xmlns":583},[585,4179,4180,4214],{},[588,4181,4182,4184,4190,4192,4198,4200,4202,4208,4210,4212],{},[598,4183,697],{},[591,4185,4186,4188],{},[594,4187,596],{},[598,4189,600],{},[845,4191,1125],{},[591,4193,4194,4196],{},[594,4195,596],{},[598,4197,697],{},[845,4199,1373],{},[598,4201,697],{},[591,4203,4204,4206],{},[594,4205,596],{},[598,4207,768],{},[845,4209,1048],{},[845,4211,1125],{},[598,4213,768],{},[602,4215,4216],{"encoding":604},"2x_1 - x_2 + 2x_3 = -3",[572,4218,4220,4278,4333,4391],{"className":4219,"ariaHidden":610},[609],[572,4221,4223,4226,4229,4269,4272,4275],{"className":4222},[614],[572,4224],{"className":4225,"style":1398},[618],[572,4227,697],{"className":4228},[623],[572,4230,4232,4235],{"className":4231},[623],[572,4233,596],{"className":4234},[623,627],[572,4236,4238],{"className":4237},[631],[572,4239,4241,4261],{"className":4240},[635,636],[572,4242,4244,4258],{"className":4243},[640],[572,4245,4247],{"className":4246,"style":645},[644],[572,4248,4249,4252],{"style":648},[572,4250],{"className":4251,"style":653},[652],[572,4253,4255],{"className":4254},[657,658,659,660],[572,4256,600],{"className":4257},[623,660],[572,4259,668],{"className":4260},[667],[572,4262,4264],{"className":4263},[640],[572,4265,4267],{"className":4266,"style":675},[644],[572,4268],{},[572,4270],{"className":4271,"style":1445},[1069],[572,4273,1125],{"className":4274},[1449],[572,4276],{"className":4277,"style":1445},[1069],[572,4279,4281,4284,4324,4327,4330],{"className":4280},[614],[572,4282],{"className":4283,"style":1459},[618],[572,4285,4287,4290],{"className":4286},[623],[572,4288,596],{"className":4289},[623,627],[572,4291,4293],{"className":4292},[631],[572,4294,4296,4316],{"className":4295},[635,636],[572,4297,4299,4313],{"className":4298},[640],[572,4300,4302],{"className":4301,"style":645},[644],[572,4303,4304,4307],{"style":648},[572,4305],{"className":4306,"style":653},[652],[572,4308,4310],{"className":4309},[657,658,659,660],[572,4311,697],{"className":4312},[623,660],[572,4314,668],{"className":4315},[667],[572,4317,4319],{"className":4318},[640],[572,4320,4322],{"className":4321,"style":675},[644],[572,4323],{},[572,4325],{"className":4326,"style":1445},[1069],[572,4328,1373],{"className":4329},[1449],[572,4331],{"className":4332,"style":1445},[1069],[572,4334,4336,4339,4342,4382,4385,4388],{"className":4335},[614],[572,4337],{"className":4338,"style":1398},[618],[572,4340,697],{"className":4341},[623],[572,4343,4345,4348],{"className":4344},[623],[572,4346,596],{"className":4347},[623,627],[572,4349,4351],{"className":4350},[631],[572,4352,4354,4374],{"className":4353},[635,636],[572,4355,4357,4371],{"className":4356},[640],[572,4358,4360],{"className":4359,"style":645},[644],[572,4361,4362,4365],{"style":648},[572,4363],{"className":4364,"style":653},[652],[572,4366,4368],{"className":4367},[657,658,659,660],[572,4369,768],{"className":4370},[623,660],[572,4372,668],{"className":4373},[667],[572,4375,4377],{"className":4376},[640],[572,4378,4380],{"className":4379,"style":675},[644],[572,4381],{},[572,4383],{"className":4384,"style":1070},[1069],[572,4386,1048],{"className":4387},[1074],[572,4389],{"className":4390,"style":1070},[1069],[572,4392,4394,4397,4400],{"className":4393},[614],[572,4395],{"className":4396,"style":1767},[618],[572,4398,1125],{"className":4399},[623],[572,4401,768],{"className":4402},[623],[951,4404,4405,4406,4612,4613,2655],{},"Ein Minuszeichen beim Normalenvektor übersehen: Bei ",[572,4407,4409,4447],{"className":4408},[575],[572,4410,4412],{"className":4411},[579],[581,4413,4414],{"xmlns":583},[585,4415,4416,4444],{},[588,4417,4418,4420,4426,4428,4434,4436,4438],{},[598,4419,697],{},[591,4421,4422,4424],{},[594,4423,596],{},[598,4425,600],{},[845,4427,1125],{},[591,4429,4430,4432],{},[594,4431,596],{},[598,4433,697],{},[845,4435,1373],{},[598,4437,697],{},[591,4439,4440,4442],{},[594,4441,596],{},[598,4443,768],{},[602,4445,4446],{"encoding":604},"2x_1 - x_2 + 2x_3",[572,4448,4450,4508,4563],{"className":4449,"ariaHidden":610},[609],[572,4451,4453,4456,4459,4499,4502,4505],{"className":4452},[614],[572,4454],{"className":4455,"style":1398},[618],[572,4457,697],{"className":4458},[623],[572,4460,4462,4465],{"className":4461},[623],[572,4463,596],{"className":4464},[623,627],[572,4466,4468],{"className":4467},[631],[572,4469,4471,4491],{"className":4470},[635,636],[572,4472,4474,4488],{"className":4473},[640],[572,4475,4477],{"className":4476,"style":645},[644],[572,4478,4479,4482],{"style":648},[572,4480],{"className":4481,"style":653},[652],[572,4483,4485],{"className":4484},[657,658,659,660],[572,4486,600],{"className":4487},[623,660],[572,4489,668],{"className":4490},[667],[572,4492,4494],{"className":4493},[640],[572,4495,4497],{"className":4496,"style":675},[644],[572,4498],{},[572,4500],{"className":4501,"style":1445},[1069],[572,4503,1125],{"className":4504},[1449],[572,4506],{"className":4507,"style":1445},[1069],[572,4509,4511,4514,4554,4557,4560],{"className":4510},[614],[572,4512],{"className":4513,"style":1459},[618],[572,4515,4517,4520],{"className":4516},[623],[572,4518,596],{"className":4519},[623,627],[572,4521,4523],{"className":4522},[631],[572,4524,4526,4546],{"className":4525},[635,636],[572,4527,4529,4543],{"className":4528},[640],[572,4530,4532],{"className":4531,"style":645},[644],[572,4533,4534,4537],{"style":648},[572,4535],{"className":4536,"style":653},[652],[572,4538,4540],{"className":4539},[657,658,659,660],[572,4541,697],{"className":4542},[623,660],[572,4544,668],{"className":4545},[667],[572,4547,4549],{"className":4548},[640],[572,4550,4552],{"className":4551,"style":675},[644],[572,4553],{},[572,4555],{"className":4556,"style":1445},[1069],[572,4558,1373],{"className":4559},[1449],[572,4561],{"className":4562,"style":1445},[1069],[572,4564,4566,4569,4572],{"className":4565},[614],[572,4567],{"className":4568,"style":1398},[618],[572,4570,697],{"className":4571},[623],[572,4573,4575,4578],{"className":4574},[623],[572,4576,596],{"className":4577},[623,627],[572,4579,4581],{"className":4580},[631],[572,4582,4584,4604],{"className":4583},[635,636],[572,4585,4587,4601],{"className":4586},[640],[572,4588,4590],{"className":4589,"style":645},[644],[572,4591,4592,4595],{"style":648},[572,4593],{"className":4594,"style":653},[652],[572,4596,4598],{"className":4597},[657,658,659,660],[572,4599,768],{"className":4600},[623,660],[572,4602,668],{"className":4603},[667],[572,4605,4607],{"className":4606},[640],[572,4608,4610],{"className":4609,"style":675},[644],[572,4611],{}," ist ",[572,4614,4616,4640],{"className":4615},[575],[572,4617,4619],{"className":4618},[579],[581,4620,4621],{"xmlns":583},[585,4622,4623,4637],{},[588,4624,4625,4631,4633,4635],{},[591,4626,4627,4629],{},[594,4628,843],{},[598,4630,697],{},[845,4632,1048],{},[845,4634,1125],{},[598,4636,600],{},[602,4638,4639],{"encoding":604},"n_2 = -1",[572,4641,4643,4698],{"className":4642,"ariaHidden":610},[609],[572,4644,4646,4649,4689,4692,4695],{"className":4645},[614],[572,4647],{"className":4648,"style":619},[618],[572,4650,4652,4655],{"className":4651},[623],[572,4653,843],{"className":4654},[623,627],[572,4656,4658],{"className":4657},[631],[572,4659,4661,4681],{"className":4660},[635,636],[572,4662,4664,4678],{"className":4663},[640],[572,4665,4667],{"className":4666,"style":645},[644],[572,4668,4669,4672],{"style":648},[572,4670],{"className":4671,"style":653},[652],[572,4673,4675],{"className":4674},[657,658,659,660],[572,4676,697],{"className":4677},[623,660],[572,4679,668],{"className":4680},[667],[572,4682,4684],{"className":4683},[640],[572,4685,4687],{"className":4686,"style":675},[644],[572,4688],{},[572,4690],{"className":4691,"style":1070},[1069],[572,4693,1048],{"className":4694},[1074],[572,4696],{"className":4697,"style":1070},[1069],[572,4699,4701,4704,4707],{"className":4700},[614],[572,4702],{"className":4703,"style":1767},[618],[572,4705,1125],{"className":4706},[623],[572,4708,600],{"className":4709},[623],[951,4711,4712,4713,4741,4742,4745,4746,4774],{},"Bei Spurpunkten nur eine Koordinate ",[572,4714,4716,4729],{"className":4715},[575],[572,4717,4719],{"className":4718},[579],[581,4720,4721],{"xmlns":583},[585,4722,4723,4727],{},[588,4724,4725],{},[598,4726,983],{},[602,4728,983],{"encoding":604},[572,4730,4732],{"className":4731,"ariaHidden":610},[609],[572,4733,4735,4738],{"className":4734},[614],[572,4736],{"className":4737,"style":995},[618],[572,4739,983],{"className":4740},[623]," setzen. Für einen Achsenschnittpunkt müssen ",[567,4743,4744],{},"zwei"," Koordinaten ",[572,4747,4749,4762],{"className":4748},[575],[572,4750,4752],{"className":4751},[579],[581,4753,4754],{"xmlns":583},[585,4755,4756,4760],{},[588,4757,4758],{},[598,4759,983],{},[602,4761,983],{"encoding":604},[572,4763,4765],{"className":4764,"ariaHidden":610},[609],[572,4766,4768,4771],{"className":4767},[614],[572,4769],{"className":4770,"style":995},[618],[572,4772,983],{"className":4773},[623]," sein.",{"title":4776,"searchDepth":4777,"depth":4777,"links":4778},"",2,[4779,4780,4781],{"id":560,"depth":4777,"text":561},{"id":1090,"depth":4777,"text":1091},{"id":3883,"depth":4777,"text":3884},[4783,4786,4789,4791,4793,4795,4797,4799],{"lhs":4784,"rhs":4785},"(x1 - p1)*n1 + (x2 - p2)*n2 + (x3 - p3)*n3 + (n1*p1 + n2*p2 + n3*p3)","n1*x1 + n2*x2 + n3*x3",{"lhs":4787,"rhs":4788},"2*1 + (-1)*3 + 2*(-1)","-3",{"lhs":4790,"rhs":4788},"2*0 - 1 + 2*(-1)",{"lhs":4792,"rhs":768},"2*1 - 1 + 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