Question

Angle between the vectors $\sqrt{3}(\overline{a}\times \overline{b})$ and $\overline{b}-(\overline{a}.\overline{b})\overline{a}$ is

Answer 1

$\left(\sqrt{3}\right(\overline{a}\times \overline{b}\left)\right).(\overline{b}-(\overline{a}.\overline{a}).\overline{a})=|\left(\sqrt{3}\right(\overline{\times }\overline{)})||\overline{b}-(\overline{a}.\overline{b})\overline{b}|\cos P$

Where $P$ is the angle them, so.

$\cos P=0$

So, $P=\pi /2$

Hence those are perpendicular.