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Question

A line makes angles α,β,γ,δ with the four diagonals of a cube. Then cos2α+cos2β+cos2γ+cos2δ is

A
43
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B
23
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C
3
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D
0
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Solution

The correct option is A 43
DC’s of diagonals OP, BQ, CS and AR are
13,13,13;13,13;13,13,13,13;13,13,13
Let dc’s of a line be l, m, n
cosα=l+m+n3cos β=lm+n3cos γ=l+mn3cos δ=l+m+n3

cos2α+cos2β+cos2γ=(l+m+n)2+(lm+n)2+(l+mn)2+(l+m+n)23=43

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