Question

The projection of the vector $2\hat{i}+\hat{j}-3\hat{k}$ on the vector $\hat{i}-2\hat{j}+\hat{k}$ is

• A. $-\frac{3}{\sqrt{14}}$
• B. $\frac{3}{\sqrt{14}}$
• C. $-\sqrt{\frac{3}{2}}$
• D. $\frac{3}{\sqrt{2}}$

Answer 1

The correct option is C $-\sqrt{\frac{3}{2}}$

Let $\overrightarrow{a}=2\hat{i}+\hat{j}-3\hat{k}$ and $\overrightarrow{b}=\hat{i}-2\hat{j}+\hat{k}$

Projection of $\overrightarrow{a}$ on $\overrightarrow{b}=\frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{b}|}$

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

$=\frac{2-2-3}{\sqrt{6}}$

$=-\frac{3}{\sqrt{6}}$

$=-\sqrt{\frac{3}{2}}$

Hence, C is the correct option.