Let u and v be two non-zero vectors in mathbb | vedclass

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(C) Given that $u$ and $v$ are non-zero vectors in $\mathbb{R}^3$.We know that the magnitude of the cross product is $|u 	imes v| = |u||v| \sin 	het

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$|u|^2|v|^2$

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(C) Given that $u$ and $v$ are non-zero vectors in $\mathbb{R}^3$.We know that the magnitude of the cross product is $|u 	imes v| = |u||v| \sin 	heta$ and the dot product is $u \cdot v = |u||v| \cos 	heta$,where $	heta$ is the angle between the vectors $u$ and $v$.Substituting these into the expression $|u 	imes v|^2 + |u \cdot v|^2$:$|u 	imes v|^2 + |u \cdot v|^2 = (|u||v| \sin 	heta)^2 + (|u||v| \cos 	heta)^2$$= |u|^2|v|^2 \sin^2 	heta + |u|^2|v|^2 \cos^2 	heta$$= |u|^2|v|^2 (\sin^2 	heta + \cos^2 	heta)$Since $\sin^2 	heta + \cos^2 	heta = 1$,we get:$= |u|^2|v|^2(1) = |u|^2|v|^2$.

Let $u$ and $v$ be two non-zero vectors in $\mathbb{R}^3$. Then $|u \times v|^2 + |u \cdot v|^2$ is equal to

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