If $\left| \overrightarrow{\mathbf{a}} ight| = 5,\ |\overrightarrow{\mathbf{b}}| = 6$ and $\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = - 25,$ then $|\overrightarrow{\mathbf{a}} imes \overrightarrow{\mathbf{b}}|$ is equal to

Question

If $\left| \overrightarrow{\mathbf{a}} ight| = 5,\ |\overrightarrow{\mathbf{b}}| = 6$ and $\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = - 25,$ then $|\overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}}|$ is equal to

Dr. Abubacker · Accepted Answer

(d)
$\left| \overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}} ight|^{2} + \left( \overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} ight)^{2} = \left| \overrightarrow{\mathbf{a}} ight|^{2}\ \ |\overrightarrow{\mathbf{b}}|^{2}$
$\Longrightarrow |\overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}}|^{2} = 25 	imes 36 - (25)^{2}$
$= 25(36 - 25)$
$= 25 	imes 11$
$\Longrightarrow |\overrightarrow{\mathbf{a}} 	imes \overrightarrow{\mathbf{b}}| = 5\sqrt{11}$

Q. If $\left| \overrightarrow{\mathbf{a}} \right| = 5,\ |\overrightarrow{\mathbf{b}}| = 6$ and $\overrightarrow{\mathbf{a}} \bullet \overrightarrow{\mathbf{b}} = - 25,$ then $|\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}|$ is equal to

Explanation

Reviewed by Dr. Abubacker

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