 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-2/10/b/solution

The direction must first be represented by a unit vector:

\hat{q} = (1, 1, 1) / 3

S \cdot \hat{q} = \frac{π a ^{2}}{2 3} .

If a vector projection is intended, multiply this scalar by

\hat{q}

proj_{q} S = \frac{π a ^{2}}{6} (1, 1, 1) .

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