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Question 204508: A body diagonal of a cube is a line through the centre joining opposite verticies. Find the angles between the body diagonals of a cube.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A body diagonal of a cube is a line through the centre joining opposite verticies. Find the angles between the body diagonals of a cube.
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Put the Origin at the center of the cube. The vertices are:
(1,1,1), (-1,1,1), (1,-1,1), etc.
All angles will be equal, finding one is sufficient.
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Find the angle between vector A i+j+k and B i+j-k
A dot B = |A|*|B|*cos(x)
|A| = |B| = sqrt(3)
A dot B = 1 + 1 - 1 = 1
cos = 1/sqrt(3)
Angle = arccos(sqrt(3)/3)
Angle = ~ 54.7356 degs
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