If $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}$ are two vectors such that $\left| \overrightarrow{\mathbf{a}} \right| + 3\sqrt{3}$, $\overrightarrow{\mathbf{b}} = 4$ and $\left| \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \right| = \sqrt{7}$, then the angle between $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{b}}$ is

Question

Dr. Abubacker · Accepted Answer

(d)
Since, $|\overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}}|^{2} = |\overrightarrow{\mathbf{a}}|^{2} + |\overrightarrow{\mathbf{b}}|^{2} + 2\ \left| \overrightarrow{\mathbf{a}} ight||\overrightarrow{\mathbf{b}}|cos\ 	heta$
$\Longrightarrow (\sqrt{7})^{2} = (3\sqrt{3})^{2} + 4^{2} + 2(3\sqrt{3})^{2}(4)\cos	heta$
$\Longrightarrow 7 = 27 + 16 + 24\sqrt{3}\cos	heta$
$\Longrightarrow \cos{	heta = - \sqrt{3}}/2$
$\Longrightarrow \ 	heta = 150{^\circ}$

Explanation

Reviewed by Dr. Abubacker

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