Question

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

• A. $\frac{18(3\hat{j}+4\hat{k})}{10\sqrt{3}}$
• B. $\frac{18(3\hat{j}+4\hat{k})}{25}$
• C. $\frac{18(3\hat{j}+4\hat{k})}{\sqrt{13}}$
• D. $3\hat{j}+\hat{k}$

Answer 1

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

Vector form of the component of a along b is
$\frac{(a.b)b}{|b^2|}=\frac{\left[\right(4\hat{i}+6\hat{j}).(3\hat{j}+4\hat{k}\left)\right](3\hat{j}+4\hat{k})}{|3\hat{j}+4\hat{k}{|}^2}=\frac{(0+18+0)(3\hat{j}+4\hat{k})}{9+16}=\frac{18}{25}(3\hat{j}+4\hat{k}).$