# Proving a vector Identity

## Homework Statement

Let the domain D be bounded by the surface S as in the divergence theorem, and assume that all fields satisfy the appropriate differentiability conditions.
Suppose that:
$$\nabla\cdot\vec{V}=0$$
$$\vec{W}=\nabla\phi with \phi = 0 on S$$
prove:
$$\int\int\int_{D}\vec{V}\cdot\vec{W}dV=0$$

This problem is in the Laplace's, Poisson's and Greens Formulas section. Truthfully I'm not sure where to even get started here. If anyone could give me a push in the right direction I would appreciate it greatly.

$$\vec{V} = curl \vec{G}$$