For which $\lambda$ is $(3\hat{i} - 6\hat{j} + 9\hat{k}) \times (\hat{i} + \lambda\hat{j} + 3\hat{k}) = \vec{0}$?

Explanation

1. 01

   The vector product is zero exactly when the vectors are parallel: $\frac{1}{3} = \frac{\lambda}{-6} = \frac{3}{9}$.

2. 02

   $\lambda = -2$.