Let $\mathbf { F } ( x , y , z ) = 3 z \mathbf { i } - 4 \mathbf { j } + y \mathbf { k }$

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = 3 z \mathbf { i } - 4 \mathbf { j } + y \mathbf { k }$ and S is $x + y + z = 1$ in the first octant. Then the flux of $\text { F }$ through S is

A) $- \frac { 4 } { 3 }$
B) $\frac { 4 } { 3 }$
C) $\frac { 4 } { 5 }$
D) $- \frac { 4 } { 5 }$
E) $- \frac { 4 } { 7 }$