The lines $\vec{r} = (\hat{i} + 3\hat{j} - 6\hat{k}) + \lambda(\hat{i} - \hat{j} + 2\hat{k})$ and $\vec{r} = (\hat{i} - 2\hat{k}) + \mu(2\hat{i} + \hat{j})$ intersect. At which point?

Explanation

1. 01

   Equate the components: $1 + \lambda = 1 + 2\mu$, $3 - \lambda = \mu$ and $-6 + 2\lambda = -2$.

2. 02

   The last gives $\lambda = 2$, then $\mu = 1$, and the first checks: $3 = 3$. The point is $(3, 1, -2)$.