The unit normal to the plane 2x +y + 2z = 6 can be expressed in the vector form as

Equation of the plane, $2x+y+2z=6$
$\therefore \text{ Normal vector, }\overrightarrow{n}=(2,1,2)$
$\begin{array}{l}\left|\overrightarrow{n}\right|=\sqrt{2^2+1^2+2^2}=3\\ \Rightarrow \text{ Unit normal vector, }\widehat{n}=\frac{\overrightarrow{n}}{\left|\overrightarrow{n}\right|}=\frac{(2,1,2)}{3}\\ \therefore \widehat{n}=\frac{2}{3}\widehat{i}+\frac{\widehat{j}}{3}+\frac{2}{3}\widehat{k}\end{array}$