 Solution

ID: 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/solution

(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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