Question

If the vectors $2\hat{i}+3\hat{j},5\hat{i}+6\hat{j},8\hat{i}+$ $\lambda$j have their initial point at $(1,1)$$thenthevalueof$\lambda$ so that the vectors terminated on one line is

• A. 5
• B. 9
• C. 4
• D. 0

Answer 1

The correct option is B 9

Since initial point of $2i+3j,5i+6j$ and $8i+\lambda j$ is $i+j$,

their terminal points will be $3i+4j,6i+7j,$and $9i+(\lambda +1)j$.

Now given all the vectors terminate on one straight line.

Hence, $3i+3j={\lambda }_1(3i+(\lambda +1-7\left)j\right)\Rightarrow {\lambda }_1=1$ and $\lambda =9$