(a) Find a vector parametric equation for the ellipse that lies on the plane $3x-y+z = -7$ and inside the cylinder $x^2 + y^2 = 64$.

$\boldsymbol{\vec{r}}(u,v) =$ for $0 \leq u \leq 8$ and $0 \leq v \leq 2\pi$.

(b) $\vec{dA} = \displaystyle \boldsymbol{\vec{r}}_u \times \boldsymbol{\vec{r}}_v =$

(c) $\displaystyle dA = \|\vec{dA}\| = \left\| \boldsymbol{\vec{r}}_u \times \boldsymbol{\vec{r}}_v \right\| =$

(d) Set up and evaluate a double integral for the surface area of the ellipse.

Surface area =