Solution
= Solution
The direction must first be represented by a <unit vector>: $\hat{\mathbf q}=(1,1,1)/\sqrt3$. The <scalar projection> of the <vector area> is therefore
$$
\boxed{\mathbf S\cdot\hat{\mathbf q}=\frac{\pi a^2}{2\sqrt3}}.
$$
If a <vector projection> is intended, multiply this scalar by $\hat{\mathbf q}$:
$$
\boxed{\operatorname{proj}_{\mathbf q}\mathbf S=\frac{\pi a^2}{6}(1,1,1)}.
$$