Find the cosine of the angle between two diagonals of a cube?

\frac{1}{3}

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\frac{2 \sqrt{2}}{3}

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\frac{1}{2}

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None of these

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Solution

The correct option is C $\frac{1}{3}$
Here the diagonals are body diagonals, one of whose direction is $(1, 1, 1)$ and the other direction is $(- 1, 1, 1)$
Now the cosine of angle between the two is $\frac{- 1 + 1 + 1}{\sqrt{3} \times \sqrt{3}}$
i.e. $\frac{1}{3}$

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