Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2018 / Paper 1 / 6 / a

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- Solution a

Solution

A space diagonal of the unit cube has displacement vector

(1, 1, 1)

. Its Euclidean norm, or two successive applications of the Pythagorean theorem, gives

d = 1^{2} + 1^{2} + 1^{2} = 3 units .

The requested diagonal joins opposite vertices;

2

would be the diagonal of a face.

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