A vector field \(\mathbf{F}\) is incompressible if \(\operatorname{div}(\mathbf{F})=0\) and is irrotational if \(\operatorname{curl}(\mathbf{F})=\mathbf{0}\).

Let \(\mathbf{F}\) be an incompressible vector field that is everywhere tangent to level surfaces of \(f\). Prove that \(f \mathbf{F}\) is incompressible.