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 1338595682 2012/06/02 09:08: 2 |\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}x_{i}y_{j}x_{k}y_{j}-\delta_{jk}x_{i}y_{j}x_{k}y_{i}\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} _________LaTeX__________________ 24 ______(________________________) <IMG SRC="../cgi-cache/20120602_084607.gif"> 現在使用可能なLaTeXコマンド一覧 \! \& \, \Cal \Cph \Cps \Cth \Delta \Gamma \Im \LaTeX \LaTeXe \Lambda \Mqqa \Mqqb \Mss \Mtt \Omega \Phi \Pi \Pr \Psi \Re \Sal \Sigma \Sph \Sps \Sth \TeX \Theta \Upsilon \Vq \Vs \Vt \Xi \_ \acute \alpha \angle \arccos \arcsin \arctan \arg \ast \backslash \bar \beta \breve \cal \cap \cdot \cdot \cdots \check \chi \circ \clubsuit \cong \cos \cosh \cot \coth \cph \cps \csc \cth \cup \ddot \ddots \deg \delta \det \diamondsuit \dim \displaystyle \div \dot \epsilon \equiv \eta \exists \exp \flat \forall \frac \gamma \gcd \geq \gg \grave \hat \heartsuit \hline \hom \hspace \inf \int \iota \kappa \ker \lambda \ldots \left \leftarrow \leftrightarrow \leq \lg \lim \liminf \limsup \ll \ln \log \mathrm \mathstrut \max \mbox \min \mp \mu \natural \neq \nonumber \not \nu \o \omega \overline \overrightarrow \par \partial \phi \pi \pm \psi \raisebox \rho \right \rightarrow \rm \sal \seq \sharp \sigma \sim \simeq \sin \sinh \spadesuit \sph \sps \sqrt \sth \subset \sum \sup \supset \surd \tan \tanh \tau \theta \tilde \times \triangle \underline \upsilon \varepsilon \varpi \varpsi \varrho \varsigma \vartheta \vdots \vec \vect \vee \vspace \wedge \widetilde \xi \zeta \{ \} \begin{array} \end{array} \begin{tabular} \end{tabular} 20120602_084607 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=mAQG-W6mQAQFTh_d_V3dvCLmJFQ9mybuCUfHWJUOy0hcnWg Sat Jun 2 09:08:02 2012