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

The correct option is A $\frac{5}{\sqrt{2}}$
Given.

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

$\overrightarrow{B}=\hat{i}+\hat{j}$

The component of $\overrightarrow{A}$ along $\overrightarrow{B}$ is,

$C=\frac{\overrightarrow{A}.\overrightarrow{B}}{|\overrightarrow{B}|}$

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

$C=\frac{2\times 1+3\times 1}{\sqrt{2}}=\frac{5}{\sqrt{2}}$

Thus, the correct option is A.