Let $S$ denote the plane surface whose boundary is the triangle with vertices at $(1,0,0),(0,1,0),(0,0,1)$ and let $F(x,y,z)=+yj+zk.$ Let $n$ denote the unit normal to $S$ having a nonnegative z$-$component. Evaluate the surface integral ${}_{S}F.ndS,$ using:

$($i$)$ the vector representation $r(u,v)=(u+v)i+(u-v)j+(1-2u)k,$

$2$

$($ii$)$ an explicit representation of the form $z=f(x,y).$