2 Mozilla/5.0 (Windows NT 6.1; WOW64; rv:12.0) Gecko/20100101 Firefox/12.0 /rde/contents/library/ps2img/cgi-bin/eqn2gif.cgi 157.118.3.12 1338591642 2012/06/02 08:00:42 |\vect{x}|^{2}|\vect{y}|^{2}&=&(\vect{x}\cdot\vect{y})^{2}+|\vect{x}\times\vect{y}|^{2}\nonumber\\ \nonumber\\ |\vect{x}\times\vect{y}|^{2}&=&(\vect{x}\times\vect{y})\cdot(\vect{x}\times\vect{y})\nonumber\\ &=&((x_{i}\vect{e}_{i})\times(y_{j}\vect{e}_{j}))\cdot((x_{k}\vect{e}_{k})\times(y_{l}\vect{e}_{l}))\nonumber\\ &=&x_{i}y_{j}x_{k}y_{l}(\vect{e}_{i}\times\vect{e}_{j})\cdot(\vect{e}_{k}\times\vect{e}_{l})\nonumber\\ &=&x_{i}y_{j}x_{k}y_{l}(\epsilon_{ijm}\vect{e}_{m})\cdot(\epsilon_{kln}\vect{e}_{n})\nonumber\\ &=&\epsilon_{ijm}\epsilon_{kln}x_{i}y_{j}x_{k}y_{l}(\vect{e}_{m}\cdot\vect{e}_{n})\nonumber\\ &=&\delta_{mn}\epsilon_{ijm}\epsilon_{kln}x_{i}y_{j}x_{k}y_{l}\nonumber\\ &=&\epsilon_{ijm}\epsilon_{klm}x_{i}y_{j}x_{k}y_{l}\nonumber\\ &=&(\delta_{ik}\delta_{jl}-\delta_{il}\delta_{jk})x_{i}y_{j}x_{k}y_{l}\nonumber\\ &=&\delta_{ik}\delta_{jl}x_{i}y_{j}x_{k}y_{l}-\delta_{il}\delta_{jk}x_{i}y_{j}x_{k}y_{l}\nonumber\\ &=&x_{i}y_{j}x_{i}y_{j}-x_{i}y_{j}x_{j}y_{i}\nonumber\\ &=&(x_{i}x_{i})(y_{j}y_{j})-(x_{i}y_{i})(x_{j}y_{j})\nonumber\\ &=&(\vect{x}\cdot\vect{x})(\vect{y}\cdot\vect{y})-(\vect{x}\cdot\vect{y})(\vect{x}\cdot\vect{y})\nonumber\\ &=&|\vect{x}|^{2}|\vect{y}|^{2}-(\vect{x}\cdot\vect{y})^{2} 3 ______(________________________) <IMG SRC="../cgi-cache/20120602_080031.gif"> 正常に処理されました 20120602_080031 http://www.facebook.com/l.php?u=http%3A%2F%2Fwww.mech.tohoku-gakuin.ac.jp%2Frde%2Fcontents%2Flibrary%2Fps2img%2Fcgi-bin%2Feqn2gif.cgi&h=pAQGHYBMGAQG3wVxneJFfL3Dj-mbxDr0v8QNe095ofq5EuQ Sat Jun 2 08:00:42 2012