Find the unit normal vectors to the plane $2x - y + 2z = 5$.
Equation of the plane is
$2x - y + 2z = 5$
Its vector equation is
$\overrightarrow{r} \cdot \left(2 \hat{i} - \hat{j} + 2 \hat{k}\right) = 5$ $\;\;\;$ [$\overrightarrow{r}$ is a vector lying in the plane.]
A normal vector to the plane is
$\overrightarrow{n} = 2 \hat{i} - \hat{j} + 2 \hat{k}$
$\therefore$ $\;$ Unit normal vectors to the plane are
$\begin{aligned}
\hat{n} & = \pm \left(\dfrac{\overrightarrow{n}}{\left|\overrightarrow{n}\right|}\right) \\\\
& = \pm \left(\dfrac{2 \hat{i} - \hat{j} + 2 \hat{k}}{\sqrt{\left(2\right)^2 + \left(-1\right)^2 + \left(2\right)^2}}\right) \\\\
& = \pm \left(\dfrac{2 \hat{i} - \hat{j} + 2 \hat{k}}{3}\right)
\end{aligned}$