Find the co-ordinates of points which trisects the line joining the points $P(-3,2,4)\text{ and }Q(0,4,7)$

Let R divides P and Q internally in the ratio 1:2

Then the co-ordinates of R

$\begin{array}{l}=\left(\frac{0-6}{1+2},\frac{4+4}{1+2},\frac{7+8}{1+2}\right)\\ =\left(-2,\frac{8}{3},5\right)\end{array}$

Again, let S divides P and Q internally in the ratio 2 :1. Then the co-ordinates of S

$\begin{array}{l}=\left(\frac{0-3}{1+2},\frac{8+2}{1+2},\frac{14+4}{1+2}\right)\\ =\left(-1,\frac{10}{3},6\right).\end{array}$