If |$\overrightarrow{\mathbf{a}}| = 10,|\overrightarrow{\mathbf{b}}| = 2\$and$\ \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = 12$ then $|\overrightarrow{\mathbf{a}} imes \overrightarrow{\mathbf{b}}|$ is equal to

Question

If |$\overrightarrow{\mathbf{a}}| = 10,|\overrightarrow{\mathbf{b}}| = 2\$and$\ \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = 12$ then $|\overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}}|$ is equal to

Dr. Abubacker · Accepted Answer

(c)
Given, $\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = 12$
$\Longrightarrow \left| \overrightarrow{\mathbf{a}} ight||\overrightarrow{\mathbf{b}}|$ $cos\ 	heta\  = 12$
$\Longrightarrow 10 	imes 2 	imes \cos{	heta = 12}$
$\Longrightarrow \cos	heta = \frac{3}{5}$
$	herefore\sin	heta = \sqrt{1 - {cos\ }^{2}	heta} = \sqrt{1 - \frac{9}{25}} = \frac{4}{5}$
$Now,\ \$
$|\overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}}| = |\overrightarrow{\mathbf{a}}||\overrightarrow{\mathbf{b}}|\ sin\ 	heta = 10 	imes 2 	imes \frac{4}{5} = 16$

Q. If |$\overrightarrow{\mathbf{a}}| = 10,|\overrightarrow{\mathbf{b}}| = 2\$and$\ \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = 12$ then $|\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}|$ is equal to

Explanation

Reviewed by Dr. Abubacker

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