Let $S$ be the cube with side length 2, faces parallel to the coordinate planes, and centered at the origin.

(a) Calculate the total flux of the constant vector field $\vec v = \,\mathit{\vec i}-3\,\mathit{\vec j}+3\,\mathit{\vec k}$ out of $S$ by computing the flux through each face separately.
flux through the face at $x=1$:
flux through the face at $y=1$:
flux through the face at $z=1$:
flux through the face at $x=-1$:
flux through the face at $y=-1$:
flux through the face at $z=-1$:

Thus the total flux is
flux =

Calculate the flux out of $S$ for any constant vector field $\vec v=a\vec i + b\vec j + c\vec k$.
flux =
(Be sure that you can explain why your answers to parts (a) and (b) make sense.)