Question

Consider a rectangular box with side lengths 1, 2 and 3.

1. We construct a (large) number of vectors by taking two different corners and computing the displacement vector between these corners. Since there are 28 different possible pairs of corners and we can take the vector pointing in either direction, there are potentially 56 different vectors (however, many of them are repeated because of the symmetry of the rectangular box). List all of the possible vectors that we obtain in this fashion.

2. Compute the smallest positive angle between any two of these vectors

Answer 1