Question

The component of vector $\overrightarrow{A}=2\hat{i}+3\hat{j}$ 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 $\frac{5}{\sqrt{2}}$

Component of $\overrightarrow{A}$ along $\overrightarrow{B}$ is given by $\frac{\overrightarrow{A}.\overrightarrow{B}}{B}$
which gives, $\frac{(2\hat{i}+3\hat{j}).(\hat{i}+\hat{j})}{\sqrt{1^2+1^2}}$, giving $\frac{5}{\sqrt{2}}$