Chapter 15.8, Problem 10ES

Use Stokes’s Theorem to evaluate ${\displaystyle \underset{C}{\oint }\text{F}.dr.}$

$\text{F(}x,y,z)=xy\text{i}+yz\text{j}+zx\text{k;}C$ is the triangle in the plane $z+y+z=1$ with vertices $(1,0,0),(0,1,0)\text{and}\text{(0,}\text{0,}\text{1)}$ with a counterclockwise orientation looking from the first octant toward the origin.