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  • What is the sum of squares of direction cosines of all the four diagonals of the cube?

What is the sum of squares of direction cosines of all the four diagonals of the cube?

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Solution: If\(l,m,n) be the direction cosine of a line

which makes angles \alpha ,eta ,gamma ,delta with these four diagonals of the cube , then

\ cosalpha =(l+m+n)/sqrt3 \ \coseta =(-l+m+n)/sqrt3\ \cosgamma =(l-m+n)/sqrt3\ \cosdelta =(l+m-n)/sqrt3

Therefore ,\ cos^2alpha +cos^2eta +cos^2gamma +cos^2delta =4/3

Posted by

Deependra Verma

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