Question

If $\overrightarrow{a}=4\hat{i}+6\hat{j}$ and $\overrightarrow{b}=3\overrightarrow{j}+4\overrightarrow{k}$ then the vector form of component of $\overrightarrow{a}$ along $\overrightarrow{b}$ is

• A. $\frac{18}{10\sqrt{3}}(3\hat{j}+4\hat{k})$
• B. $\frac{18}{25}(3\hat{j}+4\hat{k})$
• C. $\frac{18}{\sqrt{3}}(3\hat{j}+4\hat{k})$
• D. $3\hat{j}+4\hat{k}$

Answer 1

The correct option is B $\frac{18}{25}(3\hat{j}+4\hat{k})$

The component of $\overrightarrow{a}$ along $\overrightarrow{b}$ is given by
$\left(\frac{\overrightarrow{a}.\overrightarrow{b}}{|\overrightarrow{b}{|}^2}\right)\overrightarrow{b}=\frac{18}{25}(3\hat{j}+4\hat{k})$