Question

Find the component of vector $\overrightarrow{A}=(2\stackrel{\wedge }{i}+\stackrel{\wedge }{3j})$ along the direction $(\stackrel{\wedge }{i}+\stackrel{\wedge }{j})$.

• A. $-\frac{5}{\sqrt{2}}(\stackrel{\wedge }{i}-\stackrel{\wedge }{j})$
• B. $-\frac{1}{2}(\stackrel{\wedge }{i}+\stackrel{\wedge }{j})$
• C. $\frac{1}{2}(\stackrel{\wedge }{i}-\stackrel{\wedge }{j})$
• D. $\frac{5}{\sqrt{2}}(\stackrel{\wedge }{i}+\stackrel{\wedge }{j})$

Answer 1

The correct option is D $\frac{5}{\sqrt{2}}(\stackrel{\wedge }{i}+\stackrel{\wedge }{j})$

Given,

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

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

The component of vector along $\overrightarrow{B}$

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

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

$C=\frac{5}{\sqrt{2}}(\hat{i}+\hat{j})$