Question

The vectors $2\hat{i}+3\hat{j}$, $5\hat{i}+6\hat{j}$ and $8\hat{i}+\lambda \hat{j}$ have their initial values at $(1,1)$, the value of $\lambda$ so that vectors terminate on one straight line is,

• A. $0$
• B. $3$
• C. $6$
• D. $9$

Answer 1

The correct option is D $9$

$\begin{array}{c}2\hat{i}+3\hat{j},5\hat{i}+6\hat{j},8\hat{i}+\lambda \hat{j}\\ \downarrow \\ (1,1)\end{array}$

Terminal point $(3,4),(6,7),(9,\lambda +1)$

$y-4=\frac{3}{3}(x-3)$

$\Rightarrow y-4=x-3$

$\Rightarrow \lambda +1-4=9-3$

$\Rightarrow \lambda -3=6$

$\therefore \lambda =9$