$($a$)$ Find a vector parametric equation for the ellipse that lies on the plane $z-(x+3y)=-2$ and inside the cylinder $x^2+y^2=16.$

vec$(r)(u,v)=$ for $0u4$ and $0v2.$

$($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 $=$