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  4. The angle between any two diagonals of a cube is

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Q. The angle between any two diagonals of a cube is

Three Dimensional Geometry

Solution:

image
Direction ratios of $OP$ are $<\,a, a, a\,>$ or $<\,1,1,1\,>$
and those of $AL$ are $<\,-a, a, a\,>$ or $<\,-1,1,1\,>$
$\therefore \cos \theta=\frac{-1+1+1}{\sqrt{3} \cdot \sqrt{3}}=\frac{1}{3}$