Question

The component of vector $A=2\hat{i}+3\hat{j}$ along the vector
$\hat{i}+\hat{j}$ is

• A. $\frac{5}{\sqrt{2}}$
• B. $10\sqrt{2}$
• C. $5\sqrt{2}$
• D. $5$

Answer 1

The correct option is A

$\frac{5}{\sqrt{2}}$

$\frac{\overrightarrow{A}.\overrightarrow{B}}{|\overrightarrow{i}+\overrightarrow{j}|}=\frac{(2\hat{i}+3\hat{j})(\hat{i}+\hat{j})}{\sqrt{2}}=\frac{2+3}{\sqrt{2}}=\frac{5}{\sqrt{2}}$