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

Question

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

Aicharya · Accepted Answer

Given $u$ and $v$ are non zero vectors in $I R^3$. $\begin{aligned} & 	ext { To Find }|u 	imes v|^2+|u \cdot v|^2 \ & \qquad \begin{array}{l}|u|^2|v|^2 \sin ^2 	heta+|u|^2|v|^2 \cos ^2 	heta \ =|u|^2|v|^2\left(\sin ^2 	heta+\cos ^2 	hetaight) \ \quad\{\because u 	imes v=|u||v| \sin 	heta u \cdot v=|u||v| \cos 	heta\}\end{array}\end{aligned}$ $=|u|^2|v|^2$

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

Solution