Show that \(\Phi(u, v)=(2 u+1, u-v, 3 u+v)\) parametrizes the plane \(2 x-y-z=2\). Then

(a) Calculate \(\mathbf{T}_{u}, \mathbf{T}_{v}\), and \(\mathbf{N}(u, v)\).

(b) Find the area of \(\mathcal{S}=\Phi(\mathcal{D})\), where

\(\mathcal{D}=\{(u, v): 0 \leq u \leq 2,0 \leq v \leq 1\}\).

(c) Express \(f(x, y, z)=y z\) in terms of \(u\) and \(v\), and evaluate \(\iint_{\mathcal{S}} f(x, y, z) d S\).