Find the Flux of the Curl of Field F Through $\mathbf { F } = ( x - y ) \mathbf { i } + ( x - z ) \mathbf { j } + ( y - z ) \mathbf { k } ; S$

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $\mathbf { F } = ( x - y ) \mathbf { i } + ( x - z ) \mathbf { j } + ( y - z ) \mathbf { k } ; S$ is the portion of the cone $z = 3 \sqrt { x ^ { 2 } + y ^ { 2 } }$ below the plane $z = 2$

A) $- \frac { 8 } { 9 } \pi$
B) $\frac { 8 } { 9 } \pi$
C) $\frac { 16 } { 9 }$
D) $- \frac { 16 } { 9 } \pi$