(a) In R3 the vectors (k, 0, 0), (0, k, 0), and (0, 0, k) form the edges of a cube with diagonal (k, k, k) (Figure 3.3.4). Similarly, in Rn the vectors
(k, 0,0,..., 0), (0, k, 0......0)........ (0,0,0,.., k)
can be regarded as edges of a "cube" with diagonal (k, k, k,..., k). Show that each of the above edges makes an angle of θ with the diagonal, where cosθ = 1 √n.
(b) What happens to the angle ft in part (a) as the dimension of Rn approaches + ∞?