Find a unit vector perpendicular to each of the vectors vector(a + 2b) and vector(2a + b),

Question

Find a unit vector perpendicular to each of the vectors \(\vec{a}+2\vec{b}\) and \(2\vec{a}+\vec{b},\) where \(\vec{a}=3\hat{i}+2\hat{j}+2\hat{k}\) and \(\vec{b}=\hat{i}+2\hat{j}-2\hat{k}.\)

Answer 1

Now, perpendicular vector of \((\vec{a}+2\vec{b})\) and \((2\vec{a}+\vec{b})\)

Required unit vector