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

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(C) We know that for any two vectors $\vec{a}$ and $\vec{b}$,the relationship between their dot product and cross product is given by the identity: $|

Vedclass · Accepted Answer

$16$

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(C) We know that for any two vectors $\vec{a}$ and $\vec{b}$,the relationship between their dot product and cross product is given by the identity: $|\vec{a} 	imes \vec{b}|^2 + (\vec{a} \cdot \vec{b})^2 = |\vec{a}|^2 |\vec{b}|^2$ Given values are $|\vec{a}|=10$,$|\vec{b}|=2$,and $\vec{a} \cdot \vec{b}=12$. Substituting these values into the identity: $|\vec{a} 	imes \vec{b}|^2 + (12)^2 = (10)^2 (2)^2$ $|\vec{a} 	imes \vec{b}|^2 + 144 = 100 	imes 4$ $|\vec{a} 	imes \vec{b}|^2 + 144 = 400$ $|\vec{a} 	imes \vec{b}|^2 = 400 - 144$ $|\vec{a} 	imes \vec{b}|^2 = 256$ Taking the square root on both sides: $|\vec{a} 	imes \vec{b}| = \sqrt{256} = 16$ Therefore,the correct option is $C$.

If $|\vec{a}|=10, |\vec{b}|=2$ and $\vec{a} \cdot \vec{b}=12$,then $|\vec{a} \times \vec{b}|=$ . . . . . . .

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