 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/b/solution

Choose two distinct space-diagonal directions

u = (1, 1, 1)

and

v = (- 1, 1, 1)

. Their dot product is one and their norms are both

3

. Thus the acute angle between their unoriented lines is

θ = arccos \frac{1}{3} ≃ 70.5 3^{\circ} .

Any two distinct space diagonals have an absolute dot product of one when represented with components

\pm 1

, so they give the same acute angle.

 New to topics? Read the docs here!