Question

Given $\overrightarrow{A}=2\hat{i}+3\hat{j}$ and $\overrightarrow{B}=\hat{i}+\hat{j}$. The component of vector $\overrightarrow{A}$ along $\overrightarrow{B}$ is?

• A. $\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$
• B. $\frac{3}{\sqrt{2}}$
• C. $\frac{5}{\sqrt{2}}(\hat{i}+\hat{j})$
• D. $\frac{7}{\sqrt{2}}(\hat{i}+\hat{j})$

Answer 1

The correct option is C $\frac{5}{\sqrt{2}}(\hat{i}+\hat{j})$

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

Now component of A along B is

$A\cos \theta =\frac{A.B}{|B|}\overrightarrow{B}=\frac{5}{\sqrt{2}}\hat{i}+\hat{j}$

where $A.B=2+3$=5 and $|B|=\sqrt{1^2+1^2}=\sqrt{2}$