Evaluate the surface integral double integral of $S$ of $F * dS$ for the given vector field $F$ and the oriented surface $S$. In other words, find the flux of $F$ across $S$. For closed surfaces, use the positive (outward) orientation.
$$\vec{F}(x,y,z)= y\mathbf{j} - z\mathbf{k}$$ $S$ consists of the paraboloid $y = x^2 + z^2, 0 \leq y \leq 1,$ and the disk $x^2 + z^2 \leq 1, y=1$
I did $x = u\cos t, y = u^2, z =u\sin t$
So to use double integral of $$\vec{F} * dS$$
For parametrization of the paraboloid how do you find $$\vec{F} $$ to be $<0,u^2,-u\sin t>$?