(a) Find a vector parametric equation for the part of the plane $z = y-3x+67$ that lies above $\lbrack 0, 4 \rbrack \times \lbrack 0, 2 \rbrack$.

$\boldsymbol{\vec{r}}(u,v) =$ for $0 \leq u \leq 4$ and $0 \leq v \leq 2$.

(b) $\vec{dA} = \displaystyle \frac{\partial \boldsymbol{\vec{r}} }{\partial u} \times \frac{\partial \boldsymbol{\vec{r}} }{\partial v} =$

(c) $dA = \| \vec{dA} \| = \displaystyle \left\| \frac{\partial \boldsymbol{\vec{r}} }{\partial u} \times \frac{\partial \boldsymbol{\vec{r}} }{\partial v} \right\| =$

(d) Set up and evaluate a double integral for the surface area of the part of the plane $z = y-3x+67$ that lies above the square $\lbrack 0, 4 \rbrack \times \lbrack 0, 2 \rbrack$.

Surface area =

(e) A region $R$ in the $xy$-plane has area $3.8$. What is the area of the part of the plane $z = y-3x+67$ that lies above and / or below the region $R$?

Surface area =

(f) Would the method you used to answer part (e) work for a function that is not a plane? ? Yes No