For which $\lambda$ are $2\hat{i} + 3\hat{j} - \hat{k}$ and $\lambda\hat{i} - 6\hat{j} + 2\hat{k}$ parallel?

Explanation

1. 01

   Parallel vectors have proportional components: $\frac{\lambda}{2} = \frac{-6}{3} = \frac{2}{-1}$.

2. 02

   The common ratio is $-2$, so $\lambda = -4$.