Use Stoke's theorem to evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r),$ where

vec$(F)(x,y,z)=x^2$zvec$(i)+x{y}^2$vec$(j)+z^2$vec$(k)$

and $C$ is the curve of intersection of the plane $x+y+z=1$ and the cylinder $x^2+y^2=9$ oriented counterclockwise as viewed from above.

A$.\frac{81}{2}$

B$.\frac{}{2}$

C$.1$

D$.\frac{3}{8}$

E$.9$