If $|a|=13,|b|=5$ and $\bar{a} \cdot \bar{b}=60$ then $|\bar{a} imes \bar{b}|=$

Question

If $|a|=13,|b|=5$ and $\bar{a} \cdot \bar{b}=60$ then $|\bar{a} 	imes \bar{b}|=$

Aicharya · Accepted Answer

Given $|\vec{a}|=13,|\vec{b}|=5$ and $\vec{a} \cdot \vec{b}=60$ $ \cos 	heta=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}=\frac{12}{13 	imes 5}=\frac{12}{13} $ Now, $\sin ^2 	heta=1-\cos ^2 	heta=1-\frac{144}{169}=\frac{25}{169}$ $ \sin 	heta=\frac{5}{13} $ So, $\sin 	heta=\frac{|\vec{a} 	imes \vec{b}|}{|\vec{a}| \cdot|\vec{b}|}$ $ \begin{aligned} & \frac{5}{13}=\frac{|\overrightarrow{\mathrm{a}} 	imes \overrightarrow{\mathrm{b}}|}{13 	imes 5} \ & |\overrightarrow{\mathrm{a}} 	imes \overrightarrow{\mathrm{b}}|=25 \end{aligned} $

If $|a|=13,|b|=5$ and $\bar{a} \cdot \bar{b}=60$ then $|\bar{a} \times \bar{b}|=$

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