Question
Fri February 20, 2009 By:

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

Expert Reply
Fri February 20, 2009

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.

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