Discussion
For \( \mathbf{F} = x\mathbf{i} + y\mathbf{j} + z\mathbf{k} \), the flux out of any closed surface enclosing volume \( V \) is
Answer: A
The divergence is constant:
\[ \nabla \cdot \mathbf{F} \;=\; 1 + 1 + 1 \;=\; 3, \]
so the divergence theorem gives \( \iiint 3\,dV = 3V \) whatever the shape of the surface. For a sphere of radius \( a \) this is \( 3 \times \tfrac{4}{3}\pi a^{3} = 4\pi a^{3} \), matching the direct calculation
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