10-1

$\displaystyle \vA\cdot \left( \vB\times \vA\right) =0$

(38)

を証明せよ。

$\displaystyle \vA\cdot \left( \vB\times \vA\right)$	$\displaystyle = \left( A_i \ve_i\right) \cdot \left\{ \left( B_j \ve_j\right) \... ...ve_l\right) =A_i B_j A_k \vepsilon_{jkl} \delta_{il} =A_iA_kB_j \vepsilon_{ijk}$
	$\displaystyle =0,\qquad \because\, A_iA_k=A_kA_i,\,\vepsilon_{ijk}=-\vepsilon_{kji}$

著者: 茅根裕司 chinone_at_astr.tohoku.ac.jp