Triangle $ABC$ has vertices $A(3, -1, 2)$ and $B(-2, 4, 1)$, and its centroid is $G(1, 2, -1)$. What is $C$?

Explanation

1. 01

   The centroid's position vector is $\frac{\vec{a} + \vec{b} + \vec{c}}{3}$, so $\vec{c} = 3\vec{g} - \vec{a} - \vec{b}$.

2. 02

   $3(1, 2, -1) - (3, -1, 2) - (-2, 4, 1) = (2, 3, -6)$.