Question

Given $A=2\hat{i}+3\hat{j}$ and $B=\hat{i}+\hat{j}$. The component of vector A along vector B is

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{3}{\sqrt{2}}$
• C. $\frac{5}{\sqrt{2}}$
• D. $\frac{7}{\sqrt{2}}$

Answer 1

The correct option is C $\frac{5}{\sqrt{2}}$

Component of $\overline{A}$ along $\overline{B}$ = $\frac{\overline{A}.\overline{B}}{|B|}=\frac{(2\hat{i}+3\hat{j}).(\hat{i}+\hat{j})}{\sqrt{1^2+1^2}}$
$=\frac{2\hat{i}.\hat{i}+2\hat{i}.\hat{j}+3\hat{j}.\hat{i}+3\hat{j}.\hat{j}}{\sqrt{1^2+1^2}}$
$=\frac{2+0+0+3}{\sqrt{2}}=\frac{5}{\sqrt{2}}.$