(Solved): 3) Prove the following identities: a) \( (\nabla \times \vec{A}) \times \vec{B}=\vec{A}(\nabla \cdo ...

3) Prove the following identities: a) \( (\nabla \times \vec{A}) \times \vec{B}=\vec{A}(\nabla \cdot \vec{B})-(\vec{A} \cdot \nabla) \vec{B}-\vec{A} \times(\nabla \times \vec{B})-\vec{B} \times(\nabla \times \vec{A}) \). The derivative on the left hand side operates on both \( \vec{A} \) and \( \vec{B} \). b) \( \nabla \times(\nabla \times \vec{A})=\nabla(\nabla \cdot \vec{A})-\nabla^{2} \vec{A} \).