Question

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

Answer 1

\[\text{ The given vectors are parallel }.\]

\[ \therefore 3 \hat{i} - 2 \hat{j} - 4 \hat{k} = t \left( 18 \hat{i} - 12 \hat{j} - m \hat{k} \right)\]

\[ \Rightarrow 3 \hat{i} - 2 \hat{j} - 4 \hat{k} = 18t \hat{i} - 12t \hat{j} - tm \hat{k} \]

\[\text{ Comparing both sides, we get }\]

\[ 18t = 3, - 12t = - 2, - 4 = - tm\]

\[ \Rightarrow t = \frac{1}{6} \]

\[\text{ Substituting the value of m in } -4=-tm, \text{ we get }\]

\[ - 4 = - m\left( \frac{1}{6} \right)\]

\[ \therefore m = 24\]