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## 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:

[tex]\nabla\cdot\vec{V}=0[/tex]

[tex]\vec{W}=\nabla\phi with \phi = 0 on S[/tex]

prove:

[tex]\int\int\int_{D}\vec{V}\cdot\vec{W}dV=0[/tex]

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.