CBSE Class 12-science Answered
show that the angle between any two diagonals of a cube is
Asked by | 20 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 | 20 Feb, 2009, 09:19: PM
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