Question

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

• A. $\frac{18}{10\sqrt{3}}\left(3\hat{j}+4\hat{k}\right)$
• B. $\frac{18}{25}\left(3\hat{j}+4\hat{k}\right)$
• C. $\frac{18}{\sqrt{3}}\left(3\hat{j}+4\hat{k}\right)$
• D. $\frac{18}{25}\left(4\hat{i}+6\hat{j}\right)$

Answer 1

Answer: (B)

The component of $a$ along $b$
$=\left(\frac{b\cdot a}{|b{|}^2}\right)b=\frac{(3\hat{ȷ}+4\hat{k})\cdot (4\hat{ı}+6\hat{ȷ})}{|5{|}^2}(3\hat{ȷ}+4\hat{k})$
$=\frac{18}{25}(3\hat{ȷ}+4\hat{k})$