Question

Given two vectors $\overline{a}=2\overrightarrow{i}-3\overline{j}+6\overline{k},\overline{b}=-2\overrightarrow{i}+2\overline{j}-\overline{k}$ and $\lambda =\frac{\text{the projection of}\overline{a}\text{on}\overline{b}}{\text{the projection of}\overline{b}\text{on}\overline{a}}$ 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 of $\overline{a}$ an $\overline{b}=|a|\cos \theta$

Projection of $\overline{b}$ or $\overline{a}=|b|\cos \theta$

these$\theta$ is angle between $\overline{A}$ & $\overline{b}$

$\lambda =\frac{|a|\cos \theta }{|b|\cos \theta }=\frac{|a|}{|b|}$

$\overrightarrow{a}=2\hat{i}-3\hat{j}+b\hat{k}$

$|a|=\sqrt{(2{)}^2+(-3{)}^2+(6{)}^2}=\sqrt{49}=7$

$\overrightarrow{b}=-2\hat{i}+2\hat{j}-\hat{k}$

$|b|=\sqrt{(-2{)}^2+(2{)}^2+(-1{)}^2}=\sqrt{9}=3$

$\lambda =\frac{7}{3}$