The angle between $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{b}}$ is $\frac{5\pi}{6}$ and the projection of $\overrightarrow{\mathbf{a}}$ in the direction of $\overrightarrow{\mathbf{b}}$ is $\frac{- 6}{\sqrt{3}}$, then $|\overrightarrow{\mathbf{a}}|$ is equal to

Question

Dr. Abubacker · Accepted Answer

(d)
$\because\ \overrightarrow{\mathbf{a}}$ $\mathbf{\bullet}\overrightarrow{\mathbf{b}}\mathbf{=}\left| \overrightarrow{\mathbf{a}} ight|\left| \mathbf{\ }\overrightarrow{\mathbf{b}}\mathbf{\ } ight|\cos{\frac{5\pi}{6} = -}\frac{\left| \overrightarrow{\mathbf{a}} ight|\left| \mathbf{\ }\overrightarrow{\mathbf{b}}\mathbf{\ } ight|\sqrt{3}}{2}$
$	herefore\  - \frac{6}{\sqrt{3}} = - \frac{\left| \overrightarrow{\mathbf{a}} ight|\left| \mathbf{\ }\overrightarrow{\mathbf{b}}\mathbf{\ } ight|\sqrt{3}}{2\left| \overrightarrow{\mathbf{b}} ight|}$ (given condition)
$\Rightarrow \left| \overrightarrow{\mathbf{a}} ight| = \frac{6 	imes 2}{3} = 4$

Q. The angle between $\overrightarrow{\mathbf{a}}$ and $\overrightarrow{\mathbf{b}}$ is $\frac{5\pi}{6}$ and the projection of $\overrightarrow{\mathbf{a}}$ in the direction of $\overrightarrow{\mathbf{b}}$ is $\frac{- 6}{\sqrt{3}}$, then $|\overrightarrow{\mathbf{a}}|$ is equal to

Explanation

Reviewed by Dr. Abubacker

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