8-3

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

(36)

$\displaystyle \Nabla \cdot \left(\vA \times \vB \right)$	$\displaystyle = \left( \ve_i \partial_i\right) \cdot \left[ \left( A_j \ve_j\ri... ...partial_i \left(A_j B_k\right) =\vepsilon_{ijk} \partial_i \left(A_j B_k\right)$
	$\displaystyle =\vepsilon_{ijk} B_k \partial_i A_j + \vepsilon_{ijk} A_j \partia... ...\left( A_j \ve_j\right)\cdot \left( \ve_j \vepsilon_{ikj} \partial_i B_k\right)$
	$\displaystyle =\vB \cdot \left(\Nabla \times \vA\right) -\vA \cdot \left(\Nabla \times \vB\right)$