Question

Given two vectors $\overrightarrow{a}=2\hat{i}-3\hat{j}+6\hat{k},\overrightarrow{b}=-2\hat{i}+2\hat{j}-\hat{k}$ and $\lambda =\frac{\text{the projection of}\overrightarrow{a}on\overrightarrow{b}}{\text{the projection of}\overrightarrow{b}on\overrightarrow{a}}$, then the value of $\lambda$ is ?

• A. $\frac{3}{7}$
• B. $7$
• C. $3$
• D. $\frac{7}{3}$

Answer 1

The correct option is D $\frac{7}{3}$

Projection on $\overrightarrow{a}$ on $\overrightarrow{b}$ = $\frac{\overrightarrow{a}.\overrightarrow{b}}{b}$

Projection on $\overrightarrow{b}$ on $\overrightarrow{a}$ = $\frac{\overrightarrow{a}.\overrightarrow{b}}{a}$

Thus, $\lambda =\frac{a}{b}=\frac{7}{3}$