If $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}\$are unit vectors such that $\left\lbrack \overrightarrow{\mathbf{a}}\ \overrightarrow{\mathbf{b}}\ \overrightarrow{\mathbf{a}} imes \overrightarrow{\mathbf{b}} ight brack = \frac{1}{4}$, then angle between $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}$ is

Question

If $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}\$are unit vectors such that $\left\lbrack \overrightarrow{\mathbf{a}}\ \overrightarrow{\mathbf{b}}\ \overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}} ightbrack = \frac{1}{4}$, then angle between $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}$ is

Dr. Abubacker · Accepted Answer

(c)
Given,
$\left( \overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}} ight) \bullet \left( \overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}} ight) = \frac{1}{4}$
$\Longrightarrow (\left| \overrightarrow{\mathbf{a}} ight|\left| \overrightarrow{\mathbf{b}} ight|\sin{	heta)}^{2} = \frac{1}{4}$
$\Longrightarrow \ \sin^{2}	heta = \frac{1}{4}$
$\Longrightarrow \ 	heta = \frac{\pi}{6}$

Explanation

Reviewed by Dr. Abubacker

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