Question

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

• A. $0$
• B. $3$
• C. $6$
• D. $9$

Answer 1

The correct option is D $9$

$\overrightarrow{V}=2\hat{i}+3\overrightarrow{j}$
$\overrightarrow{U}=5\hat{i}+6\overrightarrow{j}$
$\overrightarrow{W}=8\hat{i}+\lambda \overrightarrow{j}$
$\overrightarrow{V}-\overrightarrow{U}=k(\overrightarrow{W}-\overrightarrow{U})$ (as they are collnear)
$(-3\hat{i}-3\hat{j})=k(3\overrightarrow{i}+(\lambda -6\left)\hat{j}\right)$)
as $\hat{i}$ & $j$ are non collienar
$-3=3k$
$k=-1$
$k(\lambda -6)=-3$
$\lambda =9$