# Prove using divergence theorem

Use the divergence theorem to show that $$\oint\oint$$s (nXF)dS = $$\int\int\int$$R ($$\nabla$$XF)dV.

The divergence theorem states: $$\oint\oint$$s (n.F)dS = $$\int\int\int$$R ($$\nabla$$.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
Homework Helper
Gold Member
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?