Question

$\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors given by $\overrightarrow{A}=2\hat{i}+3\hat{j}$ and $\overrightarrow{B}=\hat{i}+\hat{j}$. The magnitude of the component of $\overrightarrow{A}$ along $\overrightarrow{B}$ is

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

Answer 1

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

We know that,
magnitude of component of $\overrightarrow{A}$ along $\overrightarrow{B}=\frac{\overrightarrow{A}.\overrightarrow{B}}{\left|\overrightarrow{B}\right|}$
$=\frac{(2\hat{i}+3\hat{j}).(\hat{i}+\hat{j})}{\sqrt{2}}=\frac{2+3}{\sqrt{2}}=\frac{5}{\sqrt{2}}$
Hence, the correct answer is option (a).