Find unit vector perpendicular to the plane of $\mathrm{a}=2\widehat{\mathrm{i}}-2\widehat{\mathrm{j}}+\widehat{\mathrm{k}}$ and $\mathrm{b}=\widehat{\mathrm{i}}+2\widehat{\mathrm{j}}+2\widehat{\mathrm{k}}.$

$a\times b=\left|a\right|\left|b\right|\widehat{n}$ 
$\therefore \widehat{n}=\frac{a\times b}{\left|a\right|.\left|b\right|}=\frac{\left|\begin{array}{ccc}\widehat{i}& \widehat{j}& \widehat{k}\\ 2& -2& 1\\ 1& 2& 2\end{array}\right|}{\left(\sqrt{4+4+1}\sqrt{1+4+4}\right)}$ 
$=\frac{\widehat{i}(-4-2)-\widehat{j}(4-1)+\widehat{k}(4+2)}{9}$ 
$=-\frac{6}{9}\widehat{i}-\frac{3}{9}\widehat{j}+\frac{6}{9}\widehat{k}=-\frac{2}{3}\widehat{i}-\frac{1}{3}\widehat{j}+\frac{2}{3}\widehat{k}$