So for part (b), we have
\text{norm}(\nabla g(x_{Q},y_{Q},z_{Q})) = \nabla g(x_{Q},y_{Q},z_{Q}) \cdot \frac{1}{\sqrt{3}}\left(1,-1,-1\right)
This seems so tedious to solve though. It's on a practice exam my teacher gave us and his tests are very reasonable given the time limits, so I'm...