Let $\mathbf { F } ( x , y , z ) = ( y - x ) \mathbf { i } + ( x - z ) \mathbf { j } + ( x - y ) \mathbf { k }$

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = ( y - x ) \mathbf { i } + ( x - z ) \mathbf { j } + ( x - y ) \mathbf { k }$ and C be the triangle with vertices (2, 0, 0) , (0, 2, 0) , and (0, 0, 2) . Using Stokes' Theorem, $\int _ { C } \mathbf { F } \cdot \mathbf { T } d s$ is

A) -1
B) 0
C) 1
D) -2
E) 3