Question

The value of λ for which the vectors $3\hat{i}-6\hat{j}+\hat{k}\mathrm{and}2\hat{i}-4\hat{j}+\lambda \hat{k}$ are parallel is
$$\begin{gathered} \left(\mathrm{a}\right)\frac{2}{3} \\ \left(\mathrm{b}\right)\frac{3}{2} \\ \left(\mathrm{c}\right)\frac{5}{2} \\ \left(\mathrm{d}\right)\frac{2}{5} \end{gathered}$$

Answer 1

Given: the vectors $3\hat{i}-6\hat{j}+\hat{k}\mathrm{and}2\hat{i}-4\hat{j}+\lambda \hat{k}$ are parallel

$$\begin{gathered} \mathrm{The}\mathrm{vectors}3\hat{i}-6\hat{j}+\hat{k}\mathrm{and}2\hat{i}-4\hat{j}+\lambda \hat{k}\mathrm{are}\mathrm{parallel} \\ \Rightarrow \frac{3}{2}=\frac{-6}{-4}=\frac{1}{\lambda } \\ \Rightarrow \frac{3}{2}=\frac{1}{\lambda } \\ \Rightarrow \lambda =\frac{2}{3} \end{gathered}$$

​Hence, the correct option is (a).