Question

The component of vector $\overrightarrow{A}$ = 2$\hat{i}$+3$\hat{j}$ along the direction of ($\hat{i}$,$\hat{j}$) is:

• A. 1/$\sqrt{2}$
• B. -1/$\sqrt{2}$
• C. 1/2
• D. -1/2

Answer 1

Answer: (B)

-1/$\sqrt{2}$

Given : $\overrightarrow{A}=2\hat{i}+3\hat{j},$

$\overrightarrow{B}=\hat{i}-\hat{j}$ (say)
Component of A along the direction of

$\overrightarrow{B}=\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{B}$

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