(1 point) (a) Find a vector parametric equation for the ellipse that lies on the plane $x - 2y + z = -7$ and inside the cylinder $x^2 + y^2 = 49$.
$\vec{r}(u, v) = \langle u\cos v, u\sin v, -7 - u\cos v + 2u\sin v \rangle$ for $0 \le u \le 7$ and $0 \le v \le 2\pi$.
(b) $d\vec{A} = \vec{r}_u \times \vec{r}_v = $
(c) $dA = |\vec{dA}| = |\vec{r}_u \times \vec{r}_v| = \sqrt{6}u$
(d) Set up and evaluate a double integral for the surface area of the ellipse.
Surface area = $49\sqrt{6}\pi$