The point dividing the join $(3,-2,1)$ and $(-2,3,11)$ in the ratio 2 : 3 is

Let  $A=(3,-2,1),B=(-2,3,1)$

Let $P(x,y,z)$ be the point divides $\overline{AB}$ in the ratio  $m:n$

$$\begin{gathered} P=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n},\frac{m{z}_2+n{z}_1}{m+n}) \\ P=(\frac{2(-2)+3\left(3\right)}{2+3},\frac{2\left(3\right)+3(-2)}{2+3},\frac{2\left(11\right)+3\left(1\right)}{2+3}) \\ P=(\frac{-4+9}{5},\frac{6-6}{5},\frac{22+3}{5}) \\ P=(\frac{5}{5},0,\frac{25}{5}) \\ P=(1,0,5) \end{gathered}$$