Question

The unit vector in the direction of $2\hat{i}+3\hat{j}+\hat{k}$ is

• A. $\frac{2\hat{i}+3\hat{j}+\hat{k}}{\sqrt{14}}$
• B. $\frac{2\hat{i}+\hat{j}+3\hat{k}}{\sqrt{14}}$
• C. $\frac{2\hat{i}+3\hat{j}+\hat{k}}{\sqrt{12}}$
• D. $\frac{3\hat{i}+2\hat{j}+\hat{k}}{\sqrt{14}}$

Answer 1

The correct option is A $\frac{2\hat{i}+3\hat{j}+\hat{k}}{\sqrt{14}}$

Let $\overrightarrow{a}=2\hat{i}+3\hat{j}+\hat{k}$
So, $|\overrightarrow{a}|=\sqrt{2^2+3^2+1^2}=\sqrt{14}$
Thus, the unit vector is given as
$\hat{a}=\frac{\overrightarrow{a}}{|\overrightarrow{a}|}$
$\Rightarrow \hat{a}=\frac{2\hat{i}+3\hat{j}+\hat{k}}{\sqrt{14}}$