Question

If $\overline{A}=2\hat{i}+3\hat{j}-\hat{k}$ and $\overline{B}=-\hat{i}+3\hat{j}+4\hat{k}$, then projection of $\overline{A}$ on $\overline{B}$ will be:

• A. $\frac{3}{\sqrt{13}}$
• B. $\frac{3}{\sqrt{26}}$
• C. $\sqrt{\frac{3}{26}}$
• D. $\sqrt{\frac{3}{13}}$

Answer 1

The correct option is B $\frac{3}{\sqrt{26}}$

Given,

$\overrightarrow{A}=2\hat{i}+3\hat{j}-\hat{k}$

$\overrightarrow{B}=-\hat{i}+3\hat{j}+4\hat{k}$

Projection of $\overrightarrow{A}$ on $\overrightarrow{B}$ will be

$=\frac{\overrightarrow{A}.\overrightarrow{B}}{|\overrightarrow{B}|}=\frac{(2\hat{i}+3\hat{j}-\hat{k}).(-\hat{i}+3\hat{j}+4\hat{k})}{\sqrt{(-1{)}^2+(3{)}^2+(4{)}^2}}$

$=\frac{-2+9-4}{\sqrt{26}}$

$=\frac{3}{\sqrt{26}}$

The correct option is B.