Solved: (a) As shown in Figure 3.2.6, the vectors (k, 0, 0), (0, k, 0), and (0, 0, k)
Chapter 6, Problem 11(choose chapter or problem)
(a) As shown in Figure 3.2.6, the vectors (k, 0, 0), (0, k, 0), and (0, 0, k) form the edges of a cube in R3 with diagonal (k, k, k). Similarly, the vectors (k, 0, 0,..., 0), (0, k, 0,..., 0), . . . , (0, 0, 0,... , k) can be regarded as edges of a cube in Rn with diagonal (k, k, k, . . . , k). Show that each of the above edges makes an angle of with the diagonal, where cos = 1/ n. (b) (Calculus required) What happens to the angle in part (a) as the dimension of Rn approaches ?
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