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

9

Since initial point of $2 \hat{i}+3 \hat{j}, 5 \hat{i}+6 \hat{j}$ and $8 \hat{i}+\lambda \hat{j}$ is $\hat{i}+\hat{j}$, their terminal points will be $3 \hat{i}+4 \hat{j}, 6 \hat{i}+7 \hat{j}$ and $9 \hat{i}+(\lambda+1) \hat{j}$. Now given all the vectors terminate on one straight line. Hence $3 \hat{i}+3 \hat{j}=\lambda_1(3 \hat{i}+(\lambda+1-7) \hat{j}) \Rightarrow \lambda_1=1$ and $\lambda=9$

Hence (4) is correct answer.