Given that $\left| \overrightarrow{\mathbf{a}} ight| = 3,|\overrightarrow{\mathbf{b}}| = 4,|\overrightarrow{\mathbf{a}} imes \overrightarrow{\mathbf{b}}| = 10,\$then $|\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}|^{2}$ equals

Question

Given that $\left| \overrightarrow{\mathbf{a}} ight| = 3,|\overrightarrow{\mathbf{b}}| = 4,|\overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}}| = 10,\$then $|\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}|^{2}$ equals

Dr. Abubacker · Accepted Answer

(b)
Since, $|\overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}}|^{2} + |\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}|^{2}$ =$\left| \overrightarrow{\mathbf{a}} ight|^{2}\ {|\overrightarrow{\mathbf{b}}|}^{2}$
$\Longrightarrow (10)^{2} + |\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}|^{2} = (3)^{2} \bullet (4)^{2}$
$\Longrightarrow \ |\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}|^{2} = 44$

Q. Given that $\left| \overrightarrow{\mathbf{a}} \right| = 3,|\overrightarrow{\mathbf{b}}| = 4,|\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}| = 10,\$then $|\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}}|^{2}$ equals

Explanation

Reviewed by Dr. Abubacker

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