If |vec{a}|=10, |vec{b}|=2 and vec{a} cdot ve | vedclass

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(D) We know that $\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos 	heta$. Substituting the given values: $12 = 10 	imes 2 	imes \cos 	heta$. $12

Vedclass · Accepted Answer

$16$

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(D) We know that $\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos 	heta$. Substituting the given values: $12 = 10 	imes 2 	imes \cos 	heta$. $12 = 20 \cos 	heta \implies \cos 	heta = \frac{12}{20} = \frac{3}{5}$. Since $\sin^2 	heta + \cos^2 	heta = 1$,we have $\sin 	heta = \sqrt{1 - (\frac{3}{5})^2} = \sqrt{1 - \frac{9}{25}} = \sqrt{\frac{16}{25}} = \frac{4}{5}$. Now,$|\vec{a} 	imes \vec{b}| = |\vec{a}| |\vec{b}| \sin 	heta$. $|\vec{a} 	imes \vec{b}| = 10 	imes 2 	imes \frac{4}{5} = 20 	imes \frac{4}{5} = 16$.

If $|\vec{a}|=10, |\vec{b}|=2$ and $\vec{a} \cdot \vec{b}=12$,then the value of $|\vec{a} \times \vec{b}|$ is

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