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 $\overrightarrow{b}$ = $-\hat{i} + \hat{j} - \hat{k}$ .

$\dfrac{1}{\sqrt{3}} (\hat{i} + \hat{j} + \hat{k})$

${\sqrt{2}} (\hat{i} + \hat{j} + \hat{k})$

$\dfrac{1}{\sqrt{2}} (\hat{i} + \hat{j} + \hat{k})$

$\dfrac{1}{\sqrt{2}} (\hat{i} + \hat{k})$

Solution

The correct answer is

$\dfrac{1}{\sqrt{2}} (\hat{i} + \hat{k})$

Explanation

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

$\overrightarrow{a}$ +

$\overrightarrow{b}$

$\overrightarrow{n}$ =

$\dfrac{\overrightarrow{a} + \overrightarrow{b}}{|\overrightarrow{a} + \overrightarrow{b}|}$ =

$\dfrac{\hat{i} + \hat{k}}{\sqrt{1 + 1}}$ =

$\dfrac{1}{\sqrt{2}} (\hat{i} + \hat{k})$

Find the unit vector in the direction of the vector →a\overrightarrow{a} + →b\overrightarrow{b}, where →a\overrightarrow{a} = 2ˆi−ˆj+2ˆk2\hat{i} - \hat{j} + 2\hat{k} and →b\overrightarrow{b} = −ˆi+ˆj−ˆk-\hat{i} + \hat{j} - \hat{k} .