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

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

BITSATBITSAT 2014

Solution:

for a unit cube unit vector along the diagonal
$OP = \frac{1}{\sqrt{3}} (\hat{i} + \hat{j} + \hat{k})$
unit vector along the diagonal
$CD = \frac{1}{\sqrt{3}} (\hat{i} + \hat{j} - \hat{k} )$
$\therefore \cos \theta = \frac{1}{3} ( 1 + 1 -1 ) = \frac{1}{3} $
$ \therefore \tan \theta = 2 \sqrt{2}$

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