Question

If vector $\overrightarrow{a}=4\hat{i}+5\hat{j}-3\hat{k}$ and $\overrightarrow{b}=5\hat{i}+3\hat{j}+8\hat{k}$ then value of $\frac{\text{projection of vector b on a}}{\text{projection of vector a on b}}$ is :

• A. $\frac{7}{5}$
• B. $\frac{2}{7}$
• C. $\frac{5}{8}$
• D. None of these.

Answer 1

The correct option is A $\frac{7}{5}$

Projection of a vector a on other vector b, is given by $\overline{a}.\hat{b}$= $\overline{a}.\left(\frac{\overline{b}}{|\overline{b}|}\right)$,

$\overline{a}=a\hat{i}+5\hat{j}-3\hat{k}$, $\overline{b}=5\hat{i}+3\hat{j}+8\hat{k}$, $|\overline{a}|=\sqrt{50}$, $|\overline{b}|=\sqrt{98}$,

$\frac{\text{projection of vector b on a}}{\text{projection of vector a on b}}$=$\left(\frac{\overline{b}.\overline{a}}{|\overline{a}|}\right)/\left(\frac{\overline{a}.\overline{b}}{|\overline{b}|}\right)$= $\frac{|\overline{b}|}{|\overline{a}|}$= $\frac{\sqrt{98}}{\sqrt{50}}$= $\frac{7}{5}$