$(1$ point$)($a$)$ Find a vector parametric equation for the ellipse that lies on the plane $2y-3x+z=-7$ and inside the cylinder $x^2+y^2=36.$

vec$(r)(u,v)=$

$0v2$

$$ for $0u6$ and

$($b$)$ vec$(dA)=$vec$(r{)}_u$vec$(r{)}_v=$

$($c$)dA=|vec(dA)|=|vec(r{)}_u$vec$(r{)}_v|=$

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

Surface area $=$