Question
Show that the angle between two diagonals of a cube is 
Solution
Take O, a comer of cube OBLCMANP, as origin and OA, OB, OC. the three edges through it as the axes.
Let OA = OB = OC = α, then the co-ordinates of O, A, B, C are (0, 0, 0),
(a, 0. 0), (0, a, 0). (0, 0, a) respectively ; those of P, L, M, N are (a, a, a),(0, a. a), (a, 0, a), (a, a, 0) respectively.
The four diagonals are
OP, AL, BM, CN.
Consider the diagonals AL and BM
Let
be angle between AL and BM.
Similarly the angle between the other pairs of diagonals is
Let OA = OB = OC = α, then the co-ordinates of O, A, B, C are (0, 0, 0),
(a, 0. 0), (0, a, 0). (0, 0, a) respectively ; those of P, L, M, N are (a, a, a),(0, a. a), (a, 0, a), (a, a, 0) respectively.
The four diagonals are
OP, AL, BM, CN.
Consider the diagonals AL and BM
Let
be angle between AL and BM.Similarly the angle between the other pairs of diagonals is
