3-1

$\displaystyle \Nabla \times \left( \Nabla \times \vA\right) = \Nabla \left( \Nabla \cdot \vA\right) - \Nabla^2 \vA$

(6)

$\displaystyle \Nabla \times \left( \Nabla \times \vA\right)$	$\displaystyle = \left( \ve_i \partial_i\right) \times \left\{ \left( \ve_j \par... ...\right)\partial_{ij}A_k =\vepsilon_{jkl}\vepsilon_{ilm} \ve_m \partial_{ij} A_k$
	$\displaystyle =-\vepsilon_{jkl}\vepsilon_{iml} \ve_{m} \partial_{ij} A_k = -\le... ..._{ki}\ve_{m} \partial_{ij} A_k -\delta_{ji}\delta_{km}\ve_{m} \partial_{ij} A_k$
	$\displaystyle =\ve_m \partial_{mk}A_k -\partial_{ii}\left(A_k\ve_k\right) =\Nabla\left(\Nabla\cdot \vA\right) -\Nabla^2 \vA$