If $\vec{u}=2 \vec{i}+2 \vec{j}-\vec{k}$ and $\vec{v}=6 \vec{i}-3 \vec{j}+2 \vec{k}$ then a unit vec

Question

If $\vec{u}=2 \vec{i}+2 \vec{j}-\vec{k}$ and $\vec{v}=6 \vec{i}-3 \vec{j}+2 \vec{k}$ then a unit vector perpendicular to both $\vec{u}$ and $\vec{v}$ is

Professor PC Thomas Classes · Answer

Cross product $\vec{u} 	imes \vec{v}$ provides the orthogonal vector $i - 10j - 18k$. Normalizing assigns the $\frac{1}{\sqrt{425}}$ multiplier.