Chapter 6.7, Problem 349E

For the following exercises, use Stokes’ theorem to evaluate ${\displaystyle {\iint }_s\left(curlF\cdot N\right)dS}$ for the vector fields and surface.

349. A certain closed path C in plane $2x+2y+z=1$ is known to project unto unit circle $x^2+y^2=1$ in the xy-plane. Let c be a constant and let $R\left(x,y,z\right)=xi+yj+zk$ . Use Stokes’ theorem to evaluate ${\displaystyle {\int }_c\left(ck\times R\right)\cdot dS}$ .