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 $\overrightarrow{b}=\frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{b}|}=\frac{2\times 1+3\times 1}{\sqrt{1^2+1^2}}=\frac{5}{\sqrt{2}}$