The points $A(1, 2, 7)$, $B(2, 6, 3)$ and $C(3, 10, -1)$ are collinear. In what ratio does $B$ divide $AC$?

Explanation

1. 01

   $\overrightarrow{AB} = \hat{i} + 4\hat{j} - 4\hat{k}$ and $\overrightarrow{BC} = \hat{i} + 4\hat{j} - 4\hat{k}$.

2. 02

   They are equal, so $AB = BC$: $B$ is the midpoint, ratio 1 : 1.