Prove using divergence theorem

[grissom]

Use the divergence theorem to show that \oint\oints (nXF)dS = \int\int\intR (\nablaXF)dV.

The divergence theorem states: \oint\oints (n.F)dS = \int\int\intR (\nabla.F)dV.

The difference is switching from dot product to cross product. I have no idea how to start. Can someone please point me in the right direction. Any help is appreciated.

 

[gabbagabbahey]

Hint: For any constant (position independent) vector \textbf{c}, the following is true (It's worthwhile if you prove this to yourself by looking at individual components)

\textbf{c}\cdot\int\int_{\mathcal{S}}\textbf{A}dS=\int\int_{\mathcal{S}}(\textbf{c}\cdot\textbf{A})dS

What happens if you let \textbf{A}=\textbf{n}\times\textbf{F} and apply the triple scalar product rule?