show that the angle between any two diagonals of a cube is

Asked by  | 20th Feb, 2009, 05:40: PM

Expert Answer:

suppose the cube is s.t. its one vertex is origin.

and other are on positive axis (1,0,0) (1,0,0) (1,1,0) (1,1,1) (0,1,0) (0,1,1) (0,0,1) (0,1,0)

two diagonals one which join (0,0,0) and (1,1,1) and other which join (1,0,0) and (0,1,1)

direction ratios of these two diagonals are 1,1,1 and -1,1,1

so angle between these two diagonals is

cosA = 1(-1)+ 1.1+1.1 / 33
A = cos-1(1/3)

hence proved.

Answered by  | 20th Feb, 2009, 09:19: PM

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