Solution
= Solution
For a constant <vector field>, the <flux integral> is its <dot product> with the <vector area>. Thus
$$
\Phi=\mathbf F\cdot\mathbf S
=(1,1,-1)\cdot\left(-\frac12,-\frac12,-\frac12\right)
=\boxed{-\frac12}.
$$
= Solution
For a constant <vector field>, the <flux integral> is its <dot product> with the <vector area>. Thus
$$
\Phi=\mathbf F\cdot\mathbf S
=(1,1,-1)\cdot\left(-\frac12,-\frac12,-\frac12\right)
=\boxed{-\frac12}.
$$