Chapter 16.8, Problem 11E

(a) Use Stokes’ Theorem to evaluate ${\displaystyle {\int }_{c}F\cdot dr},$ where $F\left(x,y,z\right)=x^{2}zi+x{y}^{2}j+z^{2}k$ 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.

(b) Graph both the plane and the cylinder with domains chosen so that you can see the curve $C$ and the surface that you used in part (a).

(c) Find parametric equations for $C$ and use them to graph $C$.