If $|\overrightarrow{\mathbf{a}} imes \overrightarrow{\mathbf{b}}|^{2} + |\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}|^{2} = 144\ and\ \left| \overrightarrow{\mathbf{a}} ight| = 4\ then\ |\overrightarrow{\mathbf{b}}|\$ is equal to

Question

If $|\overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}}|^{2} + |\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}|^{2} = 144\ and\ \left| \overrightarrow{\mathbf{a}} ight| = 4\ then\ |\overrightarrow{\mathbf{b}}|\$ is equal to

Dr. Abubacker · Accepted Answer

(b)
Given, $|\overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}}|^{2} + |\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}|^{2} = 144$
$\Longrightarrow \left| \overrightarrow{\mathbf{a}} ight|^{2}{+ \left| \overrightarrow{\mathbf{b}} ight|}^{2}\left( \sin^{2}	heta + \cos^{2}	heta ight) = 144$
$\Longrightarrow 16\left| \overrightarrow{\mathbf{b}} ight|^{2} = 144$
$\Longrightarrow \left| \overrightarrow{\mathbf{b}} ight| = 3$

Q. If $|\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}|^{2} + |\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}|^{2} = 144\ and\ \left| \overrightarrow{\mathbf{a}} \right| = 4\ then\ |\overrightarrow{\mathbf{b}}|\$ is equal to

Explanation

Reviewed by Dr. Abubacker

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