Triangle $ABC$ has vertices $A(2, -1, 3)$, $B(5, 1, -2)$ and $C(1, 5, -8)$. What are the direction cosines of its median, taken from $A$ towards the midpoint of $BC$?

Explanation

1. 01

   The midpoint of $BC$ is $D\left(\frac{5 + 1}{2}, \frac{1 + 5}{2}, \frac{-2 - 8}{2}\right) = (3, 3, -5)$.

2. 02

   $AD$ has direction ratios $1, 4, -8$ and length $\sqrt{1 + 16 + 64} = 9$: direction cosines $\frac{1}{9}, \frac{4}{9}, -\frac{8}{9}$.