Question

If the vectors $\overrightarrow{a}=2\hat{i}-3\hat{j}$ and $\overrightarrow{b}=-6\hat{i}+m\hat{j}$ are collinear, find the value of m.

Answer 1

It is given that the vectors $\overrightarrow{a}=2\hat{i}-3\hat{j}$ and $\overrightarrow{b}=-6\hat{i}+m\hat{j}$ are collinear.

$\therefore \overrightarrow{b}=\lambda \overrightarrow{a}$ for some scalar λ

$$\begin{gathered} \Rightarrow -6\hat{i}+m\hat{j}=\lambda \left(2\hat{i}-3\hat{j}\right) \\ \Rightarrow -6\hat{i}+m\hat{j}=2\lambda \hat{i}-3\lambda \hat{j} \\ \Rightarrow -6=2\lambda \mathrm{and}m=-3\lambda \\ \Rightarrow m=-3\times \left(\frac{-6}{2}\right)=9 \end{gathered}$$

Thus, the value of m is 9.