What point divides the join of $A(2, -3, 4)$ and $B(5, 3, -2)$ internally in the ratio 1 : 2?

Explanation

1. 01

   For $m : n$ internally: $\frac{m\vec{b} + n\vec{a}}{m + n}$, with $m = 1$ on $B$'s side.

2. 02

   $\frac{(5, 3, -2) + 2(2, -3, 4)}{3} = (3, -1, 2)$.