Question

The unit vector along $2i-3j+k$ is

• A. $\frac{2i-3j+k}{\sqrt{14}}$
• B. $\frac{2i-3j+k}{\sqrt{5}}$
• C. $\frac{2i-3j+k}{\sqrt{15}}$
• D. None of these

Answer 1

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

We have $2\hat{i}-3\hat{j}+\hat{k}$

Let $u=2\hat{i}-3\hat{j}+\hat{k}$

Unit vector is of the form $\hat{u}=\frac{u}{\left|u\right|}$

$\Rightarrow \hat{u}=\frac{2\hat{i}-3\hat{j}+\hat{k}}{|2\hat{i}-3\hat{j}+\hat{k}|}$

$=\frac{2\hat{i}-3\hat{j}+\hat{k}}{\sqrt{2^2+{(-3)}^2+{\left(1\right)}^2}}$

$=\frac{2\hat{i}-3\hat{j}+\hat{k}}{\sqrt{4+9+1}}$

$\Rightarrow \hat{u}=\frac{2\hat{i}-3\hat{j}+\hat{k}}{\sqrt{14}}$