The angle between the diagonals of a cube with edges of length 1 is:

{sin}^{- 1} (1 / \sqrt{3})

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{cos}^{- 1} (1 / \sqrt{3})

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{tan}^{- 1} (1 / \sqrt{3})

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{cot}^{- 1} (1 / \sqrt{3})

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Solution

The correct option is B ${cos}^{- 1} (1 / \sqrt{3})$
Diagonal $\to d =^i +^j +^k$
$\to d \cdot^i = 1$
$\Rightarrow | \to d | |^i | cos θ = 1$
$\Rightarrow \sqrt{3} cos θ = 1$
$\Rightarrow cos θ = \frac{1}{\sqrt{3}}$

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