Let $\overline{a}=\widehat{i}+2\widehat{j}-\widehat{k}$ and $\overline{b}=\widehat{i}+\widehat{j}+\widehat{k}$ , $\overline{p}$ is a unit vector such that $\left[\overline{a}\overline{b}\overline{p}\right]$ is maximum. Then $\overline{p}$ =

$a\times b=\left|\begin{array}{l}i j k\\ 12-1\\ 111\end{array}\right|=3j-2j-k$

$\begin{array}{l}\left[abP\right]=P.(a\times b)=P(3i-2j-k)\\ \left[abP\right]=\left|P\right||a\times b|\cos \theta \\ \left[abP\right]is\max imam\\ \therefore P=\frac{a\times b}{|a\times b|}\\ P=\frac{1}{\sqrt{14}}(3i-2j-k)\end{array}$