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

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- Solution b

Solution

The direction must first be represented by a unit vector:

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

. The scalar projection of the vector area is therefore

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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