If $e_1 = \hat{i} + \hat{j} + \hat{k}$ and $e_2 = \hat{i} + \hat{j} - \hat{k}$, and $\vec{a}$ and $\vec{b}$ are two vectors such that $e_1 = 2\vec{a} + \vec{b}$ and $e_2 = \vec{a} + 2\vec{b}$, then the angle between $\vec{a}$ and $\vec{b}$ is:

Question

$\cos^{-1}\left(\frac{7}{9}\right)$

$\cos^{-1}\left(\frac{7}{11}\right)$

$\cos^{-1}\left(-\frac{7}{11}\right)$

$\cos^{-1}\left(\frac{6\sqrt{2}}{11}\right)$

Solution

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