Let \(\mathbf{F}=\langle z, 0, yangle\), and let \(\mathcal{S}\) be the oriented surface parametrized by \(\Phi(u, v)=\left(u^{2}-v, u, v^{2}ight)\) for \(0 \leq u \leq 2\), \(-1 \leq v \leq 4\). Calculate:
(a) \(\mathbf{N}\) and \(\mathbf{F} \cdot \mathbf{N}\) as functions of \(u\) and \(v\)
(b) The normal component of \(\mathbf{F}\) to the surface at \(P=(3,2,1)=\Phi(2,1)\)
(c) \(\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}\)