For which $k$ are the points $A(2, -1, 1)$, $B(4, 2, 3)$ and $C(8, k, 7)$ collinear?

Explanation

1. 01

   The direction ratios of $AB$ are $2, 3, 2$; those of $AC$ are $6, k + 1, 6$.

2. 02

   Collinear means proportional, here with factor $\frac{6}{2} = 3$: $k + 1 = 9$, so $k = 8$.