Question

If the vectors $3\hat{i}-2\hat{j}-4\hat{k}\mathrm{and}18\hat{i}-12\hat{j}-m\hat{k}$ are parallel, find the value of m.

Answer 1

$$\begin{gathered} \text{The given vectors are parallel.} \\ \therefore 3\hat{i}-2\hat{j}-4\hat{k}=t\left(18\hat{i}-12\hat{j}-m\hat{k}\right) \\ \Rightarrow 3\hat{i}-2\hat{j}-4\hat{k}=18t\hat{i}-12t\hat{j}-tm\hat{k} \\ \mathrm{Comparing}\mathrm{both}\mathrm{sides},\mathrm{we}\mathrm{get} \\ 18t=3,-12t=-2,-4=-tm \\ \Rightarrow t=\frac{1}{6} \\ \text{Substituting the value of m in -4=-}tm,\mathrm{we}\mathrm{get} \\ -4=-m\left(\frac{1}{6}\right) \\ \therefore m=24 \end{gathered}$$