In a methane $({CH}_{4})$ molecule each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the centre. In coordinates where one of the C-H bonds is in the direction of $\hat{i} + \hat{j} + \hat{k}$ , an adjacent C-H bond is in the $\hat{i} - \hat{j} - \hat{k}$ direction. Then angle between these two bonds.

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$\cos^{- 1} (- \frac{2}{3})$

$\cos^{- 1} (\frac{2}{3})$

$\cos^{- 1} (- \frac{1}{3})$

$\cos^{- 1} (\frac{1}{3})$

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Detailed Solution

$cosθ = \frac{(\hat{i} + \hat{j} + \hat{k}) . (\hat{i} - \hat{j} - \hat{k})}{\sqrt{3}}$ = $\frac{1 - 1 - 1}{3} = - \frac{1}{3}$

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