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\\vec{b}",[586,1064,1066,1120],{"className":1065,"ariaHidden":607},[624],[586,1067,1069,1073,1108,1113,1117],{"className":1068},[628],[586,1070],{"className":1071,"style":1072},[632],"height:0.7973em;vertical-align:-0.0833em;",[586,1074,1076],{"className":1075},[637,638],[586,1077,1079],{"className":1078},[642],[586,1080,1082],{"className":1081},[646],[586,1083,1085,1093],{"className":1084,"style":633},[650],[586,1086,1087,1090],{"style":653},[586,1088],{"className":1089,"style":658},[657],[586,1091,611],{"className":1092},[637,662],[586,1094,1095,1098],{"style":653},[586,1096],{"className":1097,"style":658},[657],[586,1099,1101],{"className":1100,"style":672},[671],[586,1102,1104],{"className":1103,"style":677},[676],[679,1105,1106],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,1107],{"d":690},[586,1109],{"className":1110,"style":1112},[1111],"mspace","margin-right:0.2222em;",[586,1114,1053],{"className":1115},[1116],"mbin",[586,1118],{"className":1119,"style":1112},[1111],[586,1121,1123,1126],{"className":1122},[628],[586,1124],{"className":1125,"style":723},[632],[586,1127,1129],{"className":1128},[637,638],[586,1130,1132],{"className":1131},[642],[586,1133,1135],{"className":1134},[646],[586,1136,1138,1146],{"className":1137,"style":723},[650],[586,1139,1140,1143],{"style":653},[586,1141],{"className":1142,"style":658},[657],[586,1144,708],{"className":1145},[637,662],[586,1147,1148,1151],{"style":746},[586,1149],{"className":1150,"style":658},[657],[586,1152,1154],{"className":1153,"style":672},[671],[586,1155,1157],{"className":1156,"style":677},[676],[679,1158,1159],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,1160],{"d":690}," bilden ein ",[568,1163,1164],{},"Rechtssystem"," (Rechte-Hand-Regel).",[564,1167,1168,1169,1435,1436,836,1500,1564],{},"Die Reihenfolge ist wichtig: ",[586,1170,1172,1225],{"className":1171},[589],[586,1173,1175],{"className":1174},[593],[595,1176,1177],{"xmlns":597},[599,1178,1179,1222],{},[602,1180,1181,1187,1189,1195,1198,1201,1205,1211,1213,1219],{},[605,1182,1183,1185],{"accent":607},[609,1184,708],{},[613,1186,615],{},[613,1188,1053],{},[605,1190,1191,1193],{"accent":607},[609,1192,611],{},[613,1194,615],{},[613,1196,1197],{},"=",[613,1199,1200],{},"−",[613,1202,1204],{"stretchy":1203},"false","(",[605,1206,1207,1209],{"accent":607},[609,1208,611],{},[613,1210,615],{},[613,1212,1053],{},[605,1214,1215,1217],{"accent":607},[609,1216,708],{},[613,1218,615],{},[613,1220,1221],{"stretchy":1203},")",[617,1223,1224],{"encoding":619},"\\vec{b} \\times \\vec{a} = -(\\vec{a} \\times \\vec{b})",[586,1226,1228,1279,1331,1389],{"className":1227,"ariaHidden":607},[624],[586,1229,1231,1235,1270,1273,1276],{"className":1230},[628],[586,1232],{"className":1233,"style":1234},[632],"height:1.0608em;vertical-align:-0.0833em;",[586,1236,1238],{"className":1237},[637,638],[586,1239,1241],{"className":1240},[642],[586,1242,1244],{"className":1243},[646],[586,1245,1247,1255],{"className":1246,"style":723},[650],[586,1248,1249,1252],{"style":653},[586,1250],{"className":1251,"style":658},[657],[586,1253,708],{"className":1254},[637,662],[586,1256,1257,1260],{"style":746},[586,1258],{"className":1259,"style":658},[657],[586,1261,1263],{"className":1262,"style":672},[671],[586,1264,1266],{"className":1265,"style":677},[676],[679,1267,1268],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,1269],{"d":690},[586,1271],{"className":1272,"style":1112},[1111],[586,1274,1053],{"className":1275},[1116],[586,1277],{"className":1278,"style":1112},[1111],[586,1280,1282,1285,1320,1324,1328],{"className":1281},[628],[586,1283],{"className":1284,"style":633},[632],[586,1286,1288],{"className":1287},[637,638],[586,1289,1291],{"className":1290},[642],[586,1292,1294],{"className":1293},[646],[586,1295,1297,1305],{"className":1296,"style":633},[650],[586,1298,1299,1302],{"style":653},[586,1300],{"className":1301,"style":658},[657],[586,1303,611],{"className":1304},[637,662],[586,1306,1307,1310],{"style":653},[586,1308],{"className":1309,"style":658},[657],[586,1311,1313],{"className":1312,"style":672},[671],[586,1314,1316],{"className":1315,"style":677},[676],[679,1317,1318],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,1319],{"d":690},[586,1321],{"className":1322,"style":1323},[1111],"margin-right:0.2778em;",[586,1325,1197],{"className":1326},[1327],"mrel",[586,1329],{"className":1330,"style":1323},[1111],[586,1332,1334,1338,1341,1345,1380,1383,1386],{"className":1333},[628],[586,1335],{"className":1336,"style":1337},[632],"height:1em;vertical-align:-0.25em;",[586,1339,1200],{"className":1340},[637],[586,1342,1204],{"className":1343},[1344],"mopen",[586,1346,1348],{"className":1347},[637,638],[586,1349,1351],{"className":1350},[642],[586,1352,1354],{"className":1353},[646],[586,1355,1357,1365],{"className":1356,"style":633},[650],[586,1358,1359,1362],{"style":653},[586,1360],{"className":1361,"style":658},[657],[586,1363,611],{"className":1364},[637,662],[586,1366,1367,1370],{"style":653},[586,1368],{"className":1369,"style":658},[657],[586,1371,1373],{"className":1372,"style":672},[671],[586,1374,1376],{"className":1375,"style":677},[676],[679,1377,1378],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,1379],{"d":690},[586,1381],{"className":1382,"style":1112},[1111],[586,1384,1053],{"className":1385},[1116],[586,1387],{"className":1388,"style":1112},[1111],[586,1390,1392,1396,1431],{"className":1391},[628],[586,1393],{"className":1394,"style":1395},[632],"height:1.2274em;vertical-align:-0.25em;",[586,1397,1399],{"className":1398},[637,638],[586,1400,1402],{"className":1401},[642],[586,1403,1405],{"className":1404},[646],[586,1406,1408,1416],{"className":1407,"style":723},[650],[586,1409,1410,1413],{"style":653},[586,1411],{"className":1412,"style":658},[657],[586,1414,708],{"className":1415},[637,662],[586,1417,1418,1421],{"style":746},[586,1419],{"className":1420,"style":658},[657],[586,1422,1424],{"className":1423,"style":672},[671],[586,1425,1427],{"className":1426,"style":677},[676],[679,1428,1429],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,1430],{"d":690},[586,1432,1221],{"className":1433},[1434],"mclose",". Sind ",[586,1437,1439,1456],{"className":1438},[589],[586,1440,1442],{"className":1441},[593],[595,1443,1444],{"xmlns":597},[599,1445,1446,1454],{},[602,1447,1448],{},[605,1449,1450,1452],{"accent":607},[609,1451,611],{},[613,1453,615],{},[617,1455,620],{"encoding":619},[586,1457,1459],{"className":1458,"ariaHidden":607},[624],[586,1460,1462,1465],{"className":1461},[628],[586,1463],{"className":1464,"style":633},[632],[586,1466,1468],{"className":1467},[637,638],[586,1469,1471],{"className":1470},[642],[586,1472,1474],{"className":1473},[646],[586,1475,1477,1485],{"className":1476,"style":633},[650],[586,1478,1479,1482],{"style":653},[586,1480],{"className":1481,"style":658},[657],[586,1483,611],{"className":1484},[637,662],[586,1486,1487,1490],{"style":653},[586,1488],{"className":1489,"style":658},[657],[586,1491,1493],{"className":1492,"style":672},[671],[586,1494,1496],{"className":1495,"style":677},[676],[679,1497,1498],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,1499],{"d":690},[586,1501,1503,1520],{"className":1502},[589],[586,1504,1506],{"className":1505},[593],[595,1507,1508],{"xmlns":597},[599,1509,1510,1518],{},[602,1511,1512],{},[605,1513,1514,1516],{"accent":607},[609,1515,708],{},[613,1517,615],{},[617,1519,713],{"encoding":619},[586,1521,1523],{"className":1522,"ariaHidden":607},[624],[586,1524,1526,1529],{"className":1525},[628],[586,1527],{"className":1528,"style":723},[632],[586,1530,1532],{"className":1531},[637,638],[586,1533,1535],{"className":1534},[642],[586,1536,1538],{"className":1537},[646],[586,1539,1541,1549],{"className":1540,"style":723},[650],[586,1542,1543,1546],{"style":653},[586,1544],{"className":1545,"style":658},[657],[586,1547,708],{"className":1548},[637,662],[586,1550,1551,1554],{"style":746},[586,1552],{"className":1553,"style":658},[657],[586,1555,1557],{"className":1556,"style":672},[671],[586,1558,1560],{"className":1559,"style":677},[676],[679,1561,1562],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,1563],{"d":690}," parallel, ist das Kreuzprodukt der Nullvektor.",[564,1566,1567,1568,1810,1811,1882,1883,1954],{},"Merkhilfe: Für die erste Koordinate deckt man die erste Zeile ab und rechnet „über Kreuz“ ",[586,1569,1571,1613],{"className":1570},[589],[586,1572,1574],{"className":1573},[593],[595,1575,1576],{"xmlns":597},[599,1577,1578,1610],{},[602,1579,1580,1589,1596,1598,1604],{},[1581,1582,1583,1585],"msub",{},[609,1584,611],{},[1586,1587,1588],"mn",{},"2",[1581,1590,1591,1593],{},[609,1592,708],{},[1586,1594,1595],{},"3",[613,1597,1200],{},[1581,1599,1600,1602],{},[609,1601,611],{},[1586,1603,1595],{},[1581,1605,1606,1608],{},[609,1607,708],{},[1586,1609,1588],{},[617,1611,1612],{"encoding":619},"a_2 b_3 - a_3 b_2",[586,1614,1616,1724],{"className":1615,"ariaHidden":607},[624],[586,1617,1619,1623,1675,1715,1718,1721],{"className":1618},[628],[586,1620],{"className":1621,"style":1622},[632],"height:0.8444em;vertical-align:-0.15em;",[586,1624,1626,1629],{"className":1625},[637],[586,1627,611],{"className":1628},[637,662],[586,1630,1633],{"className":1631},[1632],"msupsub",[586,1634,1637,1666],{"className":1635},[642,1636],"vlist-t2",[586,1638,1640,1661],{"className":1639},[646],[586,1641,1644],{"className":1642,"style":1643},[650],"height:0.3011em;",[586,1645,1647,1651],{"style":1646},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[586,1648],{"className":1649,"style":1650},[657],"height:2.7em;",[586,1652,1658],{"className":1653},[1654,1655,1656,1657],"sizing","reset-size6","size3","mtight",[586,1659,1588],{"className":1660},[637,1657],[586,1662,1665],{"className":1663},[1664],"vlist-s","​",[586,1667,1669],{"className":1668},[646],[586,1670,1673],{"className":1671,"style":1672},[650],"height:0.15em;",[586,1674],{},[586,1676,1678,1681],{"className":1677},[637],[586,1679,708],{"className":1680},[637,662],[586,1682,1684],{"className":1683},[1632],[586,1685,1687,1707],{"className":1686},[642,1636],[586,1688,1690,1704],{"className":1689},[646],[586,1691,1693],{"className":1692,"style":1643},[650],[586,1694,1695,1698],{"style":1646},[586,1696],{"className":1697,"style":1650},[657],[586,1699,1701],{"className":1700},[1654,1655,1656,1657],[586,1702,1595],{"className":1703},[637,1657],[586,1705,1665],{"className":1706},[1664],[586,1708,1710],{"className":1709},[646],[586,1711,1713],{"className":1712,"style":1672},[650],[586,1714],{},[586,1716],{"className":1717,"style":1112},[1111],[586,1719,1200],{"className":1720},[1116],[586,1722],{"className":1723,"style":1112},[1111],[586,1725,1727,1730,1770],{"className":1726},[628],[586,1728],{"className":1729,"style":1622},[632],[586,1731,1733,1736],{"className":1732},[637],[586,1734,611],{"className":1735},[637,662],[586,1737,1739],{"className":1738},[1632],[586,1740,1742,1762],{"className":1741},[642,1636],[586,1743,1745,1759],{"className":1744},[646],[586,1746,1748],{"className":1747,"style":1643},[650],[586,1749,1750,1753],{"style":1646},[586,1751],{"className":1752,"style":1650},[657],[586,1754,1756],{"className":1755},[1654,1655,1656,1657],[586,1757,1595],{"className":1758},[637,1657],[586,1760,1665],{"className":1761},[1664],[586,1763,1765],{"className":1764},[646],[586,1766,1768],{"className":1767,"style":1672},[650],[586,1769],{},[586,1771,1773,1776],{"className":1772},[637],[586,1774,708],{"className":1775},[637,662],[586,1777,1779],{"className":1778},[1632],[586,1780,1782,1802],{"className":1781},[642,1636],[586,1783,1785,1799],{"className":1784},[646],[586,1786,1788],{"className":1787,"style":1643},[650],[586,1789,1790,1793],{"style":1646},[586,1791],{"className":1792,"style":1650},[657],[586,1794,1796],{"className":1795},[1654,1655,1656,1657],[586,1797,1588],{"className":1798},[637,1657],[586,1800,1665],{"className":1801},[1664],[586,1803,1805],{"className":1804},[646],[586,1806,1808],{"className":1807,"style":1672},[650],[586,1809],{},". Für die zweite Koordinate beginnt man mit ",[586,1812,1814,1832],{"className":1813},[589],[586,1815,1817],{"className":1816},[593],[595,1818,1819],{"xmlns":597},[599,1820,1821,1829],{},[602,1822,1823],{},[1581,1824,1825,1827],{},[609,1826,611],{},[1586,1828,1595],{},[617,1830,1831],{"encoding":619},"a_3",[586,1833,1835],{"className":1834,"ariaHidden":607},[624],[586,1836,1838,1842],{"className":1837},[628],[586,1839],{"className":1840,"style":1841},[632],"height:0.5806em;vertical-align:-0.15em;",[586,1843,1845,1848],{"className":1844},[637],[586,1846,611],{"className":1847},[637,662],[586,1849,1851],{"className":1850},[1632],[586,1852,1854,1874],{"className":1853},[642,1636],[586,1855,1857,1871],{"className":1856},[646],[586,1858,1860],{"className":1859,"style":1643},[650],[586,1861,1862,1865],{"style":1646},[586,1863],{"className":1864,"style":1650},[657],[586,1866,1868],{"className":1867},[1654,1655,1656,1657],[586,1869,1595],{"className":1870},[637,1657],[586,1872,1665],{"className":1873},[1664],[586,1875,1877],{"className":1876},[646],[586,1878,1880],{"className":1879,"style":1672},[650],[586,1881],{},", für die dritte mit ",[586,1884,1886,1905],{"className":1885},[589],[586,1887,1889],{"className":1888},[593],[595,1890,1891],{"xmlns":597},[599,1892,1893,1902],{},[602,1894,1895],{},[1581,1896,1897,1899],{},[609,1898,611],{},[1586,1900,1901],{},"1",[617,1903,1904],{"encoding":619},"a_1",[586,1906,1908],{"className":1907,"ariaHidden":607},[624],[586,1909,1911,1914],{"className":1910},[628],[586,1912],{"className":1913,"style":1841},[632],[586,1915,1917,1920],{"className":1916},[637],[586,1918,611],{"className":1919},[637,662],[586,1921,1923],{"className":1922},[1632],[586,1924,1926,1946],{"className":1925},[642,1636],[586,1927,1929,1943],{"className":1928},[646],[586,1930,1932],{"className":1931,"style":1643},[650],[586,1933,1934,1937],{"style":1646},[586,1935],{"className":1936,"style":1650},[657],[586,1938,1940],{"className":1939},[1654,1655,1656,1657],[586,1941,1901],{"className":1942},[637,1657],[586,1944,1665],{"className":1945},[1664],[586,1947,1949],{"className":1948},[646],[586,1950,1952],{"className":1951,"style":1672},[650],[586,1953],{},"; die Indizes laufen zyklisch weiter.",[559,1956,1958],{"id":1957},"beispiele","Beispiele",[564,1960,1961,1962,836,2100,2236],{},"Für ",[586,1963,1965,2006],{"className":1964},[589],[586,1966,1968],{"className":1967},[593],[595,1969,1970],{"xmlns":597},[599,1971,1972,2003],{},[602,1973,1974,1980,1982,1984,1986,1989,1993,1995,1997,1999,2001],{},[605,1975,1976,1978],{"accent":607},[609,1977,611],{},[613,1979,615],{},[613,1981,1197],{},[613,1983,1204],{"stretchy":1203},[1586,1985,1901],{},[613,1987,1988],{"separator":607},",",[1990,1991,1992],"mtext",{}," ",[1586,1994,1588],{},[613,1996,1988],{"separator":607},[1990,1998,1992],{},[1586,2000,1595],{},[613,2002,1221],{"stretchy":1203},[617,2004,2005],{"encoding":619},"\\vec{a} = (1,\\ 2,\\ 3)",[586,2007,2009,2059],{"className":2008,"ariaHidden":607},[624],[586,2010,2012,2015,2050,2053,2056],{"className":2011},[628],[586,2013],{"className":2014,"style":633},[632],[586,2016,2018],{"className":2017},[637,638],[586,2019,2021],{"className":2020},[642],[586,2022,2024],{"className":2023},[646],[586,2025,2027,2035],{"className":2026,"style":633},[650],[586,2028,2029,2032],{"style":653},[586,2030],{"className":2031,"style":658},[657],[586,2033,611],{"className":2034},[637,662],[586,2036,2037,2040],{"style":653},[586,2038],{"className":2039,"style":658},[657],[586,2041,2043],{"className":2042,"style":672},[671],[586,2044,2046],{"className":2045,"style":677},[676],[679,2047,2048],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,2049],{"d":690},[586,2051],{"className":2052,"style":1323},[1111],[586,2054,1197],{"className":2055},[1327],[586,2057],{"className":2058,"style":1323},[1111],[586,2060,2062,2065,2068,2071,2075,2078,2082,2085,2088,2091,2094,2097],{"className":2061},[628],[586,2063],{"className":2064,"style":1337},[632],[586,2066,1204],{"className":2067},[1344],[586,2069,1901],{"className":2070},[637],[586,2072,1988],{"className":2073},[2074],"mpunct",[586,2076,1992],{"className":2077},[1111],[586,2079],{"className":2080,"style":2081},[1111],"margin-right:0.1667em;",[586,2083,1588],{"className":2084},[637],[586,2086,1988],{"className":2087},[2074],[586,2089,1992],{"className":2090},[1111],[586,2092],{"className":2093,"style":2081},[1111],[586,2095,1595],{"className":2096},[637],[586,2098,1221],{"className":2099},[1434],[586,2101,2103,2144],{"className":2102},[589],[586,2104,2106],{"className":2105},[593],[595,2107,2108],{"xmlns":597},[599,2109,2110,2141],{},[602,2111,2112,2118,2120,2122,2125,2127,2129,2132,2134,2136,2139],{},[605,2113,2114,2116],{"accent":607},[609,2115,708],{},[613,2117,615],{},[613,2119,1197],{},[613,2121,1204],{"stretchy":1203},[1586,2123,2124],{},"4",[613,2126,1988],{"separator":607},[1990,2128,1992],{},[1586,2130,2131],{},"5",[613,2133,1988],{"separator":607},[1990,2135,1992],{},[1586,2137,2138],{},"6",[613,2140,1221],{"stretchy":1203},[617,2142,2143],{"encoding":619},"\\vec{b} = (4,\\ 5,\\ 6)",[586,2145,2147,2197],{"className":2146,"ariaHidden":607},[624],[586,2148,2150,2153,2188,2191,2194],{"className":2149},[628],[586,2151],{"className":2152,"style":723},[632],[586,2154,2156],{"className":2155},[637,638],[586,2157,2159],{"className":2158},[642],[586,2160,2162],{"className":2161},[646],[586,2163,2165,2173],{"className":2164,"style":723},[650],[586,2166,2167,2170],{"style":653},[586,2168],{"className":2169,"style":658},[657],[586,2171,708],{"className":2172},[637,662],[586,2174,2175,2178],{"style":746},[586,2176],{"className":2177,"style":658},[657],[586,2179,2181],{"className":2180,"style":672},[671],[586,2182,2184],{"className":2183,"style":677},[676],[679,2185,2186],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,2187],{"d":690},[586,2189],{"className":2190,"style":1323},[1111],[586,2192,1197],{"className":2193},[1327],[586,2195],{"className":2196,"style":1323},[1111],[586,2198,2200,2203,2206,2209,2212,2215,2218,2221,2224,2227,2230,2233],{"className":2199},[628],[586,2201],{"className":2202,"style":1337},[632],[586,2204,1204],{"className":2205},[1344],[586,2207,2124],{"className":2208},[637],[586,2210,1988],{"className":2211},[2074],[586,2213,1992],{"className":2214},[1111],[586,2216],{"className":2217,"style":2081},[1111],[586,2219,2131],{"className":2220},[637],[586,2222,1988],{"className":2223},[2074],[586,2225,1992],{"className":2226},[1111],[586,2228],{"className":2229,"style":2081},[1111],[586,2231,2138],{"className":2232},[637],[586,2234,1221],{"className":2235},[1434],":",[586,2238,2241],{"className":2239},[2240],"katex-display",[586,2242,2244,2398],{"className":2243},[589],[586,2245,2247],{"className":2246},[593],[595,2248,2250],{"xmlns":597,"display":2249},"block",[599,2251,2252,2395],{},[602,2253,2254,2260,2262,2268,2270,2353,2355],{},[605,2255,2256,2258],{"accent":607},[609,2257,611],{},[613,2259,615],{},[613,2261,1053],{},[605,2263,2264,2266],{"accent":607},[609,2265,708],{},[613,2267,615],{},[613,2269,1197],{},[602,2271,2272,2274,2351],{},[613,2273,1204],{"fence":607},[2275,2276,2280,2307,2329],"mtable",{"rowspacing":2277,"columnalign":2278,"columnspacing":2279},"0.16em","center","1em",[2281,2282,2283],"mtr",{},[2284,2285,2286],"mtd",{},[2287,2288,2290],"mstyle",{"scriptlevel":2289,"displaystyle":1203},"0",[602,2291,2292,2294,2297,2299,2301,2303,2305],{},[1586,2293,1588],{},[613,2295,2296],{},"⋅",[1586,2298,2138],{},[613,2300,1200],{},[1586,2302,1595],{},[613,2304,2296],{},[1586,2306,2131],{},[2281,2308,2309],{},[2284,2310,2311],{},[2287,2312,2313],{"scriptlevel":2289,"displaystyle":1203},[602,2314,2315,2317,2319,2321,2323,2325,2327],{},[1586,2316,1595],{},[613,2318,2296],{},[1586,2320,2124],{},[613,2322,1200],{},[1586,2324,1901],{},[613,2326,2296],{},[1586,2328,2138],{},[2281,2330,2331],{},[2284,2332,2333],{},[2287,2334,2335],{"scriptlevel":2289,"displaystyle":1203},[602,2336,2337,2339,2341,2343,2345,2347,2349],{},[1586,2338,1901],{},[613,2340,2296],{},[1586,2342,2131],{},[613,2344,1200],{},[1586,2346,1588],{},[613,2348,2296],{},[1586,2350,2124],{},[613,2352,1221],{"fence":607},[613,2354,1197],{},[602,2356,2357,2359,2393],{},[613,2358,1204],{"fence":607},[2275,2360,2361,2373,2381],{"rowspacing":2277,"columnalign":2278,"columnspacing":2279},[2281,2362,2363],{},[2284,2364,2365],{},[2287,2366,2367],{"scriptlevel":2289,"displaystyle":1203},[602,2368,2369,2371],{},[613,2370,1200],{},[1586,2372,1595],{},[2281,2374,2375],{},[2284,2376,2377],{},[2287,2378,2379],{"scriptlevel":2289,"displaystyle":1203},[1586,2380,2138],{},[2281,2382,2383],{},[2284,2384,2385],{},[2287,2386,2387],{"scriptlevel":2289,"displaystyle":1203},[602,2388,2389,2391],{},[613,2390,1200],{},[1586,2392,1595],{},[613,2394,1221],{"fence":607},[617,2396,2397],{"encoding":619},"\\vec{a} \\times \\vec{b} = \\begin{pmatrix} 2 \\cdot 6 - 3 \\cdot 5 \\\\ 3 \\cdot 4 - 1 \\cdot 6 \\\\ 1 \\cdot 5 - 2 \\cdot 4 \\end{pmatrix} = \\begin{pmatrix} -3 \\\\ 6 \\\\ -3 \\end{pmatrix}",[586,2399,2401,2451,2501,2781],{"className":2400,"ariaHidden":607},[624],[586,2402,2404,2407,2442,2445,2448],{"className":2403},[628],[586,2405],{"className":2406,"style":1072},[632],[586,2408,2410],{"className":2409},[637,638],[586,2411,2413],{"className":2412},[642],[586,2414,2416],{"className":2415},[646],[586,2417,2419,2427],{"className":2418,"style":633},[650],[586,2420,2421,2424],{"style":653},[586,2422],{"className":2423,"style":658},[657],[586,2425,611],{"className":2426},[637,662],[586,2428,2429,2432],{"style":653},[586,2430],{"className":2431,"style":658},[657],[586,2433,2435],{"className":2434,"style":672},[671],[586,2436,2438],{"className":2437,"style":677},[676],[679,2439,2440],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,2441],{"d":690},[586,2443],{"className":2444,"style":1112},[1111],[586,2446,1053],{"className":2447},[1116],[586,2449],{"className":2450,"style":1112},[1111],[586,2452,2454,2457,2492,2495,2498],{"className":2453},[628],[586,2455],{"className":2456,"style":723},[632],[586,2458,2460],{"className":2459},[637,638],[586,2461,2463],{"className":2462},[642],[586,2464,2466],{"className":2465},[646],[586,2467,2469,2477],{"className":2468,"style":723},[650],[586,2470,2471,2474],{"style":653},[586,2472],{"className":2473,"style":658},[657],[586,2475,708],{"className":2476},[637,662],[586,2478,2479,2482],{"style":746},[586,2480],{"className":2481,"style":658},[657],[586,2483,2485],{"className":2484,"style":672},[671],[586,2486,2488],{"className":2487,"style":677},[676],[679,2489,2490],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,2491],{"d":690},[586,2493],{"className":2494,"style":1323},[1111],[586,2496,1197],{"className":2497},[1327],[586,2499],{"className":2500,"style":1323},[1111],[586,2502,2504,2508,2772,2775,2778],{"className":2503},[628],[586,2505],{"className":2506,"style":2507},[632],"height:3.6em;vertical-align:-1.55em;",[586,2509,2512,2560,2734],{"className":2510},[2511],"minner",[586,2513,2515],{"className":2514},[1344],[586,2516,2520],{"className":2517},[2518,2519],"delimsizing","mult",[586,2521,2523,2551],{"className":2522},[642,1636],[586,2524,2526,2548],{"className":2525},[646],[586,2527,2530],{"className":2528,"style":2529},[650],"height:2.05em;",[586,2531,2533,2537],{"style":2532},"top:-4.05em;",[586,2534],{"className":2535,"style":2536},[657],"height:5.6em;",[586,2538,2540],{"style":2539},"width:0.875em;height:3.6em;",[679,2541,2545],{"xmlns":681,"width":2542,"height":2543,"viewBox":2544},"0.875em","3.6em","0 0 875 3600",[688,2546],{"d":2547},"M863,9c0,-2,-2,-5,-6,-9c0,0,-17,0,-17,0c-12.7,0,-19.3,0.3,-20,1\nc-5.3,5.3,-10.3,11,-15,17c-242.7,294.7,-395.3,682,-458,1162c-21.3,163.3,-33.3,349,\n-36,557 l0,84c0.2,6,0,26,0,60c2,159.3,10,310.7,24,454c53.3,528,210,\n949.7,470,1265c4.7,6,9.7,11.7,15,17c0.7,0.7,7,1,19,1c0,0,18,0,18,0c4,-4,6,-7,6,-9\nc0,-2.7,-3.3,-8.7,-10,-18c-135.3,-192.7,-235.5,-414.3,-300.5,-665c-65,-250.7,-102.5,\n-544.7,-112.5,-882c-2,-104,-3,-167,-3,-189\nl0,-92c0,-162.7,5.7,-314,17,-454c20.7,-272,63.7,-513,129,-723c65.3,\n-210,155.3,-396.3,270,-559c6.7,-9.3,10,-15.3,10,-18z",[586,2549,1665],{"className":2550},[1664],[586,2552,2554],{"className":2553},[646],[586,2555,2558],{"className":2556,"style":2557},[650],"height:1.55em;",[586,2559],{},[586,2561,2563],{"className":2562},[637],[586,2564,2566],{"className":2565},[2275],[586,2567,2570],{"className":2568},[2569],"col-align-c",[586,2571,2573,2726],{"className":2572},[642,1636],[586,2574,2576,2723],{"className":2575},[646],[586,2577,2579,2627,2675],{"className":2578,"style":2529},[650],[586,2580,2582,2585],{"style":2581},"top:-4.21em;",[586,2583],{"className":2584,"style":658},[657],[586,2586,2588,2591,2594,2597,2600,2603,2606,2609,2612,2615,2618,2621,2624],{"className":2587},[637],[586,2589,1588],{"className":2590},[637],[586,2592],{"className":2593,"style":1112},[1111],[586,2595,2296],{"className":2596},[1116],[586,2598],{"className":2599,"style":1112},[1111],[586,2601,2138],{"className":2602},[637],[586,2604],{"className":2605,"style":1112},[1111],[586,2607,1200],{"className":2608},[1116],[586,2610],{"className":2611,"style":1112},[1111],[586,2613,1595],{"className":2614},[637],[586,2616],{"className":2617,"style":1112},[1111],[586,2619,2296],{"className":2620},[1116],[586,2622],{"className":2623,"style":1112},[1111],[586,2625,2131],{"className":2626},[637],[586,2628,2630,2633],{"style":2629},"top:-3.01em;",[586,2631],{"className":2632,"style":658},[657],[586,2634,2636,2639,2642,2645,2648,2651,2654,2657,2660,2663,2666,2669,2672],{"className":2635},[637],[586,2637,1595],{"className":2638},[637],[586,2640],{"className":2641,"style":1112},[1111],[586,2643,2296],{"className":2644},[1116],[586,2646],{"className":2647,"style":1112},[1111],[586,2649,2124],{"className":2650},[637],[586,2652],{"className":2653,"style":1112},[1111],[586,2655,1200],{"className":2656},[1116],[586,2658],{"className":2659,"style":1112},[1111],[586,2661,1901],{"className":2662},[637],[586,2664],{"className":2665,"style":1112},[1111],[586,2667,2296],{"className":2668},[1116],[586,2670],{"className":2671,"style":1112},[1111],[586,2673,2138],{"className":2674},[637],[586,2676,2678,2681],{"style":2677},"top:-1.81em;",[586,2679],{"className":2680,"style":658},[657],[586,2682,2684,2687,2690,2693,2696,2699,2702,2705,2708,2711,2714,2717,2720],{"className":2683},[637],[586,2685,1901],{"className":2686},[637],[586,2688],{"className":2689,"style":1112},[1111],[586,2691,2296],{"className":2692},[1116],[586,2694],{"className":2695,"style":1112},[1111],[586,2697,2131],{"className":2698},[637],[586,2700],{"className":2701,"style":1112},[1111],[586,2703,1200],{"className":2704},[1116],[586,2706],{"className":2707,"style":1112},[1111],[586,2709,1588],{"className":2710},[637],[586,2712],{"className":2713,"style":1112},[1111],[586,2715,2296],{"className":2716},[1116],[586,2718],{"className":2719,"style":1112},[1111],[586,2721,2124],{"className":2722},[637],[586,2724,1665],{"className":2725},[1664],[586,2727,2729],{"className":2728},[646],[586,2730,2732],{"className":2731,"style":2557},[650],[586,2733],{},[586,2735,2737],{"className":2736},[1434],[586,2738,2740],{"className":2739},[2518,2519],[586,2741,2743,2764],{"className":2742},[642,1636],[586,2744,2746,2761],{"className":2745},[646],[586,2747,2749],{"className":2748,"style":2529},[650],[586,2750,2751,2754],{"style":2532},[586,2752],{"className":2753,"style":2536},[657],[586,2755,2756],{"style":2539},[679,2757,2758],{"xmlns":681,"width":2542,"height":2543,"viewBox":2544},[688,2759],{"d":2760},"M76,0c-16.7,0,-25,3,-25,9c0,2,2,6.3,6,13c21.3,28.7,42.3,60.3,\n63,95c96.7,156.7,172.8,332.5,228.5,527.5c55.7,195,92.8,416.5,111.5,664.5\nc11.3,139.3,17,290.7,17,454c0,28,1.7,43,3.3,45l0,9\nc-3,4,-3.3,16.7,-3.3,38c0,162,-5.7,313.7,-17,455c-18.7,248,-55.8,469.3,-111.5,664\nc-55.7,194.7,-131.8,370.3,-228.5,527c-20.7,34.7,-41.7,66.3,-63,95c-2,3.3,-4,7,-6,11\nc0,7.3,5.7,11,17,11c0,0,11,0,11,0c9.3,0,14.3,-0.3,15,-1c5.3,-5.3,10.3,-11,15,-17\nc242.7,-294.7,395.3,-681.7,458,-1161c21.3,-164.7,33.3,-350.7,36,-558\nl0,-144c-2,-159.3,-10,-310.7,-24,-454c-53.3,-528,-210,-949.7,\n-470,-1265c-4.7,-6,-9.7,-11.7,-15,-17c-0.7,-0.7,-6.7,-1,-18,-1z",[586,2762,1665],{"className":2763},[1664],[586,2765,2767],{"className":2766},[646],[586,2768,2770],{"className":2769,"style":2557},[650],[586,2771],{},[586,2773],{"className":2774,"style":1323},[1111],[586,2776,1197],{"className":2777},[1327],[586,2779],{"className":2780,"style":1323},[1111],[586,2782,2784,2787],{"className":2783},[628],[586,2785],{"className":2786,"style":2507},[632],[586,2788,2790,2827,2895],{"className":2789},[2511],[586,2791,2793],{"className":2792},[1344],[586,2794,2796],{"className":2795},[2518,2519],[586,2797,2799,2819],{"className":2798},[642,1636],[586,2800,2802,2816],{"className":2801},[646],[586,2803,2805],{"className":2804,"style":2529},[650],[586,2806,2807,2810],{"style":2532},[586,2808],{"className":2809,"style":2536},[657],[586,2811,2812],{"style":2539},[679,2813,2814],{"xmlns":681,"width":2542,"height":2543,"viewBox":2544},[688,2815],{"d":2547},[586,2817,1665],{"className":2818},[1664],[586,2820,2822],{"className":2821},[646],[586,2823,2825],{"className":2824,"style":2557},[650],[586,2826],{},[586,2828,2830],{"className":2829},[637],[586,2831,2833],{"className":2832},[2275],[586,2834,2836],{"className":2835},[2569],[586,2837,2839,2887],{"className":2838},[642,1636],[586,2840,2842,2884],{"className":2841},[646],[586,2843,2845,2859,2870],{"className":2844,"style":2529},[650],[586,2846,2847,2850],{"style":2581},[586,2848],{"className":2849,"style":658},[657],[586,2851,2853,2856],{"className":2852},[637],[586,2854,1200],{"className":2855},[637],[586,2857,1595],{"className":2858},[637],[586,2860,2861,2864],{"style":2629},[586,2862],{"className":2863,"style":658},[657],[586,2865,2867],{"className":2866},[637],[586,2868,2138],{"className":2869},[637],[586,2871,2872,2875],{"style":2677},[586,2873],{"className":2874,"style":658},[657],[586,2876,2878,2881],{"className":2877},[637],[586,2879,1200],{"className":2880},[637],[586,2882,1595],{"className":2883},[637],[586,2885,1665],{"className":2886},[1664],[586,2888,2890],{"className":2889},[646],[586,2891,2893],{"className":2892,"style":2557},[650],[586,2894],{},[586,2896,2898],{"className":2897},[1434],[586,2899,2901],{"className":2900},[2518,2519],[586,2902,2904,2924],{"className":2903},[642,1636],[586,2905,2907,2921],{"className":2906},[646],[586,2908,2910],{"className":2909,"style":2529},[650],[586,2911,2912,2915],{"style":2532},[586,2913],{"className":2914,"style":2536},[657],[586,2916,2917],{"style":2539},[679,2918,2919],{"xmlns":681,"width":2542,"height":2543,"viewBox":2544},[688,2920],{"d":2760},[586,2922,1665],{"className":2923},[1664],[586,2925,2927],{"className":2926},[646],[586,2928,2930],{"className":2929,"style":2557},[650],[586,2931],{},[564,2933,2934,2935,836,3129,3320],{},"Probe mit dem Skalarprodukt: ",[586,2936,2938,2989],{"className":2937},[589],[586,2939,2941],{"className":2940},[593],[595,2942,2943],{"xmlns":597},[599,2944,2945,2986],{},[602,2946,2947,2949,2951,2953,2955,2957,2959,2962,2964,2966,2968,2970,2972,2974,2976,2978,2980,2982,2984],{},[613,2948,1204],{"stretchy":1203},[613,2950,1200],{},[1586,2952,1595],{},[613,2954,1221],{"stretchy":1203},[613,2956,2296],{},[1586,2958,1901],{},[613,2960,2961],{},"+",[1586,2963,2138],{},[613,2965,2296],{},[1586,2967,1588],{},[613,2969,2961],{},[613,2971,1204],{"stretchy":1203},[613,2973,1200],{},[1586,2975,1595],{},[613,2977,1221],{"stretchy":1203},[613,2979,2296],{},[1586,2981,1595],{},[613,2983,1197],{},[1586,2985,2289],{},[617,2987,2988],{"encoding":619},"(-3) \\cdot 1 + 6 \\cdot 2 + (-3) \\cdot 3 = 0",[586,2990,2992,3019,3038,3057,3075,3102,3120],{"className":2991,"ariaHidden":607},[624],[586,2993,2995,2998,3001,3004,3007,3010,3013,3016],{"className":2994},[628],[586,2996],{"className":2997,"style":1337},[632],[586,2999,1204],{"className":3000},[1344],[586,3002,1200],{"className":3003},[637],[586,3005,1595],{"className":3006},[637],[586,3008,1221],{"className":3009},[1434],[586,3011],{"className":3012,"style":1112},[1111],[586,3014,2296],{"className":3015},[1116],[586,3017],{"className":3018,"style":1112},[1111],[586,3020,3022,3026,3029,3032,3035],{"className":3021},[628],[586,3023],{"className":3024,"style":3025},[632],"height:0.7278em;vertical-align:-0.0833em;",[586,3027,1901],{"className":3028},[637],[586,3030],{"className":3031,"style":1112},[1111],[586,3033,2961],{"className":3034},[1116],[586,3036],{"className":3037,"style":1112},[1111],[586,3039,3041,3045,3048,3051,3054],{"className":3040},[628],[586,3042],{"className":3043,"style":3044},[632],"height:0.6444em;",[586,3046,2138],{"className":3047},[637],[586,3049],{"className":3050,"style":1112},[1111],[586,3052,2296],{"className":3053},[1116],[586,3055],{"className":3056,"style":1112},[1111],[586,3058,3060,3063,3066,3069,3072],{"className":3059},[628],[586,3061],{"className":3062,"style":3025},[632],[586,3064,1588],{"className":3065},[637],[586,3067],{"className":3068,"style":1112},[1111],[586,3070,2961],{"className":3071},[1116],[586,3073],{"className":3074,"style":1112},[1111],[586,3076,3078,3081,3084,3087,3090,3093,3096,3099],{"className":3077},[628],[586,3079],{"className":3080,"style":1337},[632],[586,3082,1204],{"className":3083},[1344],[586,3085,1200],{"className":3086},[637],[586,3088,1595],{"className":3089},[637],[586,3091,1221],{"className":3092},[1434],[586,3094],{"className":3095,"style":1112},[1111],[586,3097,2296],{"className":3098},[1116],[586,3100],{"className":3101,"style":1112},[1111],[586,3103,3105,3108,3111,3114,3117],{"className":3104},[628],[586,3106],{"className":3107,"style":3044},[632],[586,3109,1595],{"className":3110},[637],[586,3112],{"className":3113,"style":1323},[1111],[586,3115,1197],{"className":3116},[1327],[586,3118],{"className":3119,"style":1323},[1111],[586,3121,3123,3126],{"className":3122},[628],[586,3124],{"className":3125,"style":3044},[632],[586,3127,2289],{"className":3128},[637],[586,3130,3132,3182],{"className":3131},[589],[586,3133,3135],{"className":3134},[593],[595,3136,3137],{"xmlns":597},[599,3138,3139,3179],{},[602,3140,3141,3143,3145,3147,3149,3151,3153,3155,3157,3159,3161,3163,3165,3167,3169,3171,3173,3175,3177],{},[613,3142,1204],{"stretchy":1203},[613,3144,1200],{},[1586,3146,1595],{},[613,3148,1221],{"stretchy":1203},[613,3150,2296],{},[1586,3152,2124],{},[613,3154,2961],{},[1586,3156,2138],{},[613,3158,2296],{},[1586,3160,2131],{},[613,3162,2961],{},[613,3164,1204],{"stretchy":1203},[613,3166,1200],{},[1586,3168,1595],{},[613,3170,1221],{"stretchy":1203},[613,3172,2296],{},[1586,3174,2138],{},[613,3176,1197],{},[1586,3178,2289],{},[617,3180,3181],{"encoding":619},"(-3) \\cdot 4 + 6 \\cdot 5 + (-3) \\cdot 6 = 0",[586,3183,3185,3212,3230,3248,3266,3293,3311],{"className":3184,"ariaHidden":607},[624],[586,3186,3188,3191,3194,3197,3200,3203,3206,3209],{"className":3187},[628],[586,3189],{"className":3190,"style":1337},[632],[586,3192,1204],{"className":3193},[1344],[586,3195,1200],{"className":3196},[637],[586,3198,1595],{"className":3199},[637],[586,3201,1221],{"className":3202},[1434],[586,3204],{"className":3205,"style":1112},[1111],[586,3207,2296],{"className":3208},[1116],[586,3210],{"className":3211,"style":1112},[1111],[586,3213,3215,3218,3221,3224,3227],{"className":3214},[628],[586,3216],{"className":3217,"style":3025},[632],[586,3219,2124],{"className":3220},[637],[586,3222],{"className":3223,"style":1112},[1111],[586,3225,2961],{"className":3226},[1116],[586,3228],{"className":3229,"style":1112},[1111],[586,3231,3233,3236,3239,3242,3245],{"className":3232},[628],[586,3234],{"className":3235,"style":3044},[632],[586,3237,2138],{"className":3238},[637],[586,3240],{"className":3241,"style":1112},[1111],[586,3243,2296],{"className":3244},[1116],[586,3246],{"className":3247,"style":1112},[1111],[586,3249,3251,3254,3257,3260,3263],{"className":3250},[628],[586,3252],{"className":3253,"style":3025},[632],[586,3255,2131],{"className":3256},[637],[586,3258],{"className":3259,"style":1112},[1111],[586,3261,2961],{"className":3262},[1116],[586,3264],{"className":3265,"style":1112},[1111],[586,3267,3269,3272,3275,3278,3281,3284,3287,3290],{"className":3268},[628],[586,3270],{"className":3271,"style":1337},[632],[586,3273,1204],{"className":3274},[1344],[586,3276,1200],{"className":3277},[637],[586,3279,1595],{"className":3280},[637],[586,3282,1221],{"className":3283},[1434],[586,3285],{"className":3286,"style":1112},[1111],[586,3288,2296],{"className":3289},[1116],[586,3291],{"className":3292,"style":1112},[1111],[586,3294,3296,3299,3302,3305,3308],{"className":3295},[628],[586,3297],{"className":3298,"style":3044},[632],[586,3300,2138],{"className":3301},[637],[586,3303],{"className":3304,"style":1323},[1111],[586,3306,1197],{"className":3307},[1327],[586,3309],{"className":3310,"style":1323},[1111],[586,3312,3314,3317],{"className":3313},[628],[586,3315],{"className":3316,"style":3044},[632],[586,3318,2289],{"className":3319},[637],". Das Ergebnis steht also auf beiden Vektoren senkrecht.",[559,3322,3324],{"id":3323},"typische-fehler","Typische Fehler",[575,3326,3327,3782,3785,3817],{},[578,3328,3329,3330,3555,3556,3781],{},"Das Vorzeichen in der mittleren Koordinate falsch: Sie lautet ",[586,3331,3333,3371],{"className":3332},[589],[586,3334,3336],{"className":3335},[593],[595,3337,3338],{"xmlns":597},[599,3339,3340,3368],{},[602,3341,3342,3348,3354,3356,3362],{},[1581,3343,3344,3346],{},[609,3345,611],{},[1586,3347,1595],{},[1581,3349,3350,3352],{},[609,3351,708],{},[1586,3353,1901],{},[613,3355,1200],{},[1581,3357,3358,3360],{},[609,3359,611],{},[1586,3361,1901],{},[1581,3363,3364,3366],{},[609,3365,708],{},[1586,3367,1595],{},[617,3369,3370],{"encoding":619},"a_3 b_1 - a_1 b_3",[586,3372,3374,3469],{"className":3373,"ariaHidden":607},[624],[586,3375,3377,3380,3420,3460,3463,3466],{"className":3376},[628],[586,3378],{"className":3379,"style":1622},[632],[586,3381,3383,3386],{"className":3382},[637],[586,3384,611],{"className":3385},[637,662],[586,3387,3389],{"className":3388},[1632],[586,3390,3392,3412],{"className":3391},[642,1636],[586,3393,3395,3409],{"className":3394},[646],[586,3396,3398],{"className":3397,"style":1643},[650],[586,3399,3400,3403],{"style":1646},[586,3401],{"className":3402,"style":1650},[657],[586,3404,3406],{"className":3405},[1654,1655,1656,1657],[586,3407,1595],{"className":3408},[637,1657],[586,3410,1665],{"className":3411},[1664],[586,3413,3415],{"className":3414},[646],[586,3416,3418],{"className":3417,"style":1672},[650],[586,3419],{},[586,3421,3423,3426],{"className":3422},[637],[586,3424,708],{"className":3425},[637,662],[586,3427,3429],{"className":3428},[1632],[586,3430,3432,3452],{"className":3431},[642,1636],[586,3433,3435,3449],{"className":3434},[646],[586,3436,3438],{"className":3437,"style":1643},[650],[586,3439,3440,3443],{"style":1646},[586,3441],{"className":3442,"style":1650},[657],[586,3444,3446],{"className":3445},[1654,1655,1656,1657],[586,3447,1901],{"className":3448},[637,1657],[586,3450,1665],{"className":3451},[1664],[586,3453,3455],{"className":3454},[646],[586,3456,3458],{"className":3457,"style":1672},[650],[586,3459],{},[586,3461],{"className":3462,"style":1112},[1111],[586,3464,1200],{"className":3465},[1116],[586,3467],{"className":3468,"style":1112},[1111],[586,3470,3472,3475,3515],{"className":3471},[628],[586,3473],{"className":3474,"style":1622},[632],[586,3476,3478,3481],{"className":3477},[637],[586,3479,611],{"className":3480},[637,662],[586,3482,3484],{"className":3483},[1632],[586,3485,3487,3507],{"className":3486},[642,1636],[586,3488,3490,3504],{"className":3489},[646],[586,3491,3493],{"className":3492,"style":1643},[650],[586,3494,3495,3498],{"style":1646},[586,3496],{"className":3497,"style":1650},[657],[586,3499,3501],{"className":3500},[1654,1655,1656,1657],[586,3502,1901],{"className":3503},[637,1657],[586,3505,1665],{"className":3506},[1664],[586,3508,3510],{"className":3509},[646],[586,3511,3513],{"className":3512,"style":1672},[650],[586,3514],{},[586,3516,3518,3521],{"className":3517},[637],[586,3519,708],{"className":3520},[637,662],[586,3522,3524],{"className":3523},[1632],[586,3525,3527,3547],{"className":3526},[642,1636],[586,3528,3530,3544],{"className":3529},[646],[586,3531,3533],{"className":3532,"style":1643},[650],[586,3534,3535,3538],{"style":1646},[586,3536],{"className":3537,"style":1650},[657],[586,3539,3541],{"className":3540},[1654,1655,1656,1657],[586,3542,1595],{"className":3543},[637,1657],[586,3545,1665],{"className":3546},[1664],[586,3548,3550],{"className":3549},[646],[586,3551,3553],{"className":3552,"style":1672},[650],[586,3554],{},", nicht ",[586,3557,3559,3597],{"className":3558},[589],[586,3560,3562],{"className":3561},[593],[595,3563,3564],{"xmlns":597},[599,3565,3566,3594],{},[602,3567,3568,3574,3580,3582,3588],{},[1581,3569,3570,3572],{},[609,3571,611],{},[1586,3573,1901],{},[1581,3575,3576,3578],{},[609,3577,708],{},[1586,3579,1595],{},[613,3581,1200],{},[1581,3583,3584,3586],{},[609,3585,611],{},[1586,3587,1595],{},[1581,3589,3590,3592],{},[609,3591,708],{},[1586,3593,1901],{},[617,3595,3596],{"encoding":619},"a_1 b_3 - a_3 b_1",[586,3598,3600,3695],{"className":3599,"ariaHidden":607},[624],[586,3601,3603,3606,3646,3686,3689,3692],{"className":3602},[628],[586,3604],{"className":3605,"style":1622},[632],[586,3607,3609,3612],{"className":3608},[637],[586,3610,611],{"className":3611},[637,662],[586,3613,3615],{"className":3614},[1632],[586,3616,3618,3638],{"className":3617},[642,1636],[586,3619,3621,3635],{"className":3620},[646],[586,3622,3624],{"className":3623,"style":1643},[650],[586,3625,3626,3629],{"style":1646},[586,3627],{"className":3628,"style":1650},[657],[586,3630,3632],{"className":3631},[1654,1655,1656,1657],[586,3633,1901],{"className":3634},[637,1657],[586,3636,1665],{"className":3637},[1664],[586,3639,3641],{"className":3640},[646],[586,3642,3644],{"className":3643,"style":1672},[650],[586,3645],{},[586,3647,3649,3652],{"className":3648},[637],[586,3650,708],{"className":3651},[637,662],[586,3653,3655],{"className":3654},[1632],[586,3656,3658,3678],{"className":3657},[642,1636],[586,3659,3661,3675],{"className":3660},[646],[586,3662,3664],{"className":3663,"style":1643},[650],[586,3665,3666,3669],{"style":1646},[586,3667],{"className":3668,"style":1650},[657],[586,3670,3672],{"className":3671},[1654,1655,1656,1657],[586,3673,1595],{"className":3674},[637,1657],[586,3676,1665],{"className":3677},[1664],[586,3679,3681],{"className":3680},[646],[586,3682,3684],{"className":3683,"style":1672},[650],[586,3685],{},[586,3687],{"className":3688,"style":1112},[1111],[586,3690,1200],{"className":3691},[1116],[586,3693],{"className":3694,"style":1112},[1111],[586,3696,3698,3701,3741],{"className":3697},[628],[586,3699],{"className":3700,"style":1622},[632],[586,3702,3704,3707],{"className":3703},[637],[586,3705,611],{"className":3706},[637,662],[586,3708,3710],{"className":3709},[1632],[586,3711,3713,3733],{"className":3712},[642,1636],[586,3714,3716,3730],{"className":3715},[646],[586,3717,3719],{"className":3718,"style":1643},[650],[586,3720,3721,3724],{"style":1646},[586,3722],{"className":3723,"style":1650},[657],[586,3725,3727],{"className":3726},[1654,1655,1656,1657],[586,3728,1595],{"className":3729},[637,1657],[586,3731,1665],{"className":3732},[1664],[586,3734,3736],{"className":3735},[646],[586,3737,3739],{"className":3738,"style":1672},[650],[586,3740],{},[586,3742,3744,3747],{"className":3743},[637],[586,3745,708],{"className":3746},[637,662],[586,3748,3750],{"className":3749},[1632],[586,3751,3753,3773],{"className":3752},[642,1636],[586,3754,3756,3770],{"className":3755},[646],[586,3757,3759],{"className":3758,"style":1643},[650],[586,3760,3761,3764],{"style":1646},[586,3762],{"className":3763,"style":1650},[657],[586,3765,3767],{"className":3766},[1654,1655,1656,1657],[586,3768,1901],{"className":3769},[637,1657],[586,3771,1665],{"className":3772},[1664],[586,3774,3776],{"className":3775},[646],[586,3777,3779],{"className":3778,"style":1672},[650],[586,3780],{},".",[578,3783,3784],{},"Die Reihenfolge der Faktoren vertauschen und das Vorzeichen nicht anpassen.",[578,3786,3787,3788,3816],{},"Das Kreuzprodukt für ebene Vektoren (2D) verwenden. Dort gibt es kein Kreuzprodukt; man kann die Vektoren aber mit der dritten Koordinate ",[586,3789,3791,3804],{"className":3790},[589],[586,3792,3794],{"className":3793},[593],[595,3795,3796],{"xmlns":597},[599,3797,3798,3802],{},[602,3799,3800],{},[1586,3801,2289],{},[617,3803,2289],{"encoding":619},[586,3805,3807],{"className":3806,"ariaHidden":607},[624],[586,3808,3810,3813],{"className":3809},[628],[586,3811],{"className":3812,"style":3044},[632],[586,3814,2289],{"className":3815},[637]," in den Raum einbetten.",[578,3818,3819,3820,3884,3885,3949,3950,3978],{},"Keine Probe machen: Das Skalarprodukt mit ",[586,3821,3823,3840],{"className":3822},[589],[586,3824,3826],{"className":3825},[593],[595,3827,3828],{"xmlns":597},[599,3829,3830,3838],{},[602,3831,3832],{},[605,3833,3834,3836],{"accent":607},[609,3835,611],{},[613,3837,615],{},[617,3839,620],{"encoding":619},[586,3841,3843],{"className":3842,"ariaHidden":607},[624],[586,3844,3846,3849],{"className":3845},[628],[586,3847],{"className":3848,"style":633},[632],[586,3850,3852],{"className":3851},[637,638],[586,3853,3855],{"className":3854},[642],[586,3856,3858],{"className":3857},[646],[586,3859,3861,3869],{"className":3860,"style":633},[650],[586,3862,3863,3866],{"style":653},[586,3864],{"className":3865,"style":658},[657],[586,3867,611],{"className":3868},[637,662],[586,3870,3871,3874],{"style":653},[586,3872],{"className":3873,"style":658},[657],[586,3875,3877],{"className":3876,"style":672},[671],[586,3878,3880],{"className":3879,"style":677},[676],[679,3881,3882],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,3883],{"d":690}," und mit ",[586,3886,3888,3905],{"className":3887},[589],[586,3889,3891],{"className":3890},[593],[595,3892,3893],{"xmlns":597},[599,3894,3895,3903],{},[602,3896,3897],{},[605,3898,3899,3901],{"accent":607},[609,3900,708],{},[613,3902,615],{},[617,3904,713],{"encoding":619},[586,3906,3908],{"className":3907,"ariaHidden":607},[624],[586,3909,3911,3914],{"className":3910},[628],[586,3912],{"className":3913,"style":723},[632],[586,3915,3917],{"className":3916},[637,638],[586,3918,3920],{"className":3919},[642],[586,3921,3923],{"className":3922},[646],[586,3924,3926,3934],{"className":3925,"style":723},[650],[586,3927,3928,3931],{"style":653},[586,3929],{"className":3930,"style":658},[657],[586,3932,708],{"className":3933},[637,662],[586,3935,3936,3939],{"style":746},[586,3937],{"className":3938,"style":658},[657],[586,3940,3942],{"className":3941,"style":672},[671],[586,3943,3945],{"className":3944,"style":677},[676],[679,3946,3947],{"xmlns":681,"width":682,"height":683,"style":684,"viewBox":685,"preserveAspectRatio":686},[688,3948],{"d":690}," muss jeweils ",[586,3951,3953,3966],{"className":3952},[589],[586,3954,3956],{"className":3955},[593],[595,3957,3958],{"xmlns":597},[599,3959,3960,3964],{},[602,3961,3962],{},[1586,3963,2289],{},[617,3965,2289],{"encoding":619},[586,3967,3969],{"className":3968,"ariaHidden":607},[624],[586,3970,3972,3975],{"className":3971},[628],[586,3973],{"className":3974,"style":3044},[632],[586,3976,2289],{"className":3977},[637]," ergeben.",{"title":3980,"searchDepth":3981,"depth":3981,"links":3982},"",2,[3983,3984,3985],{"id":561,"depth":3981,"text":562},{"id":1957,"depth":3981,"text":1958},{"id":3323,"depth":3981,"text":3324},[3987,3989,3991,3994,3997,4000,4002,4004,4006],{"lhs":3988,"rhs":2289},"a1*(a2*b3 - a3*b2) + a2*(a3*b1 - a1*b3) + a3*(a1*b2 - a2*b1)",{"lhs":3990,"rhs":2289},"b1*(a2*b3 - a3*b2) + b2*(a3*b1 - a1*b3) + b3*(a1*b2 - a2*b1)",{"lhs":3992,"rhs":3993},"b2*a3 - b3*a2","-(a2*b3 - a3*b2)",{"lhs":3995,"rhs":3996},"cross([a1, a2, a3], [b1, b2, b3])[2]","a3*b1 - a1*b3",{"lhs":3998,"rhs":3999},"2*6 - 3*5","-3",{"lhs":4001,"rhs":2138},"3*4 - 1*6",{"lhs":4003,"rhs":3999},"1*5 - 2*4",{"lhs":4005,"rhs":2289},"(-3)*1 + 6*2 + (-3)*3",{"lhs":4007,"rhs":2289},"(-3)*4 + 6*5 + (-3)*6","\\vec{a}, \\vec{b} \\in \\mathbb{R}^3","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>∈\u003C\u002Fmo>\u003Cmsup>\u003Cmi mathvariant=\"double-struck\">R\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{a}, \\vec{b} \\in \\mathbb{R}^3\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.1719em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2355em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 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mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\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=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">∈\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8141em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathbb\">R\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8141em;\">\u003Cspan style=\"top:-3.063em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","cross-product","\\vec{a} \\times \\vec{b} = \\begin{pmatrix} a_2 b_3 - a_3 b_2 \\\\ a_3 b_1 - a_1 b_3 \\\\ a_1 b_2 - a_2 b_1 \\end{pmatrix}","\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>\u003Cmover accent=\"true\">\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>×\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmrow>\u003Cmo fence=\"true\">(\u003C\u002Fmo>\u003Cmtable rowspacing=\"0.16em\" columnalign=\"center\" columnspacing=\"1em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"false\">\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cmo fence=\"true\">)\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\vec{a} \\times \\vec{b} = \\begin{pmatrix} a_2 b_3 - a_3 b_2 \\\\ a_3 b_1 - a_1 b_3 \\\\ a_1 b_2 - a_2 b_1 \\end{pmatrix}\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:0.7973em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord 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mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.2634em;\">\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 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viewBox=\"0 0 875 3600\">\u003Cpath d=\"M863,9c0,-2,-2,-5,-6,-9c0,0,-17,0,-17,0c-12.7,0,-19.3,0.3,-20,1\nc-5.3,5.3,-10.3,11,-15,17c-242.7,294.7,-395.3,682,-458,1162c-21.3,163.3,-33.3,349,\n-36,557 l0,84c0.2,6,0,26,0,60c2,159.3,10,310.7,24,454c53.3,528,210,\n949.7,470,1265c4.7,6,9.7,11.7,15,17c0.7,0.7,7,1,19,1c0,0,18,0,18,0c4,-4,6,-7,6,-9\nc0,-2.7,-3.3,-8.7,-10,-18c-135.3,-192.7,-235.5,-414.3,-300.5,-665c-65,-250.7,-102.5,\n-544.7,-112.5,-882c-2,-104,-3,-167,-3,-189\nl0,-92c0,-162.7,5.7,-314,17,-454c20.7,-272,63.7,-513,129,-723c65.3,\n-210,155.3,-396.3,270,-559c6.7,-9.3,10,-15.3,10,-18z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.55em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan 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