Question

A and B are vectors.
D is del.

Prove that
a) D.(DxA)=0
b) Dx(DA)=0
c) D.(AxB)=B.(DxA)-A.(DxB)

Answer 1

a) \[\nabla \cdot(\nabla \times \vec A)=0\]
b) \[\nabla \times(\nabla \vec A)=0\]
c) \[\nabla\cdot(\vec A\times\vec B)=\vec B\cdot(\nabla \times \vec A)-\vec A\cdot(\nabla\times \vec B)\]

Answer 2

it has a lengthy proof man...