Find the unit vector in the direction of the vector $\overrightarrow{a}$ + $\overrightarrow{b}$, where $\overrightarrow{a}$ = $2\hat{i} - \hat{j} + 2\hat{k}$ and $\overrightarrow{b}$ = $-\hat{i} + \hat{j} - \hat{k} $.

The correct answer is $\dfrac{1}{\sqrt{2}} (\hat{i} + \hat{k})$

Given $\overrightarrow{a}$ = $2\hat{i} - \hat{j} + 2\hat{k}$ and $\overrightarrow{b}$ = $-\hat{i} + \hat{j} - \hat{k} $

∴ $\overrightarrow{a}$ + $\overrightarrow{b}$ = $\hat{i} + \hat{k}$

The unit vector in the direction of the vector $\overrightarrow{a}$ + $\overrightarrow{b}$

$\overrightarrow{n}$ = $\dfrac{\overrightarrow{a} + \overrightarrow{b}}{|\overrightarrow{a} + \overrightarrow{b}|}$ = $\dfrac{\hat{i} + \hat{k}}{\sqrt{1 + 1}}$ =
$\dfrac{1}{\sqrt{2}} (\hat{i} + \hat{k})$