Let A(2, 1, -3) and B(5, -8, 3) be two given points. Find the coordinates of the point of trisection of the segment AB.
The coordinates of point $R$ that divides the line segment joining points $P\left(x_{1}\right.$,$\left.\mathrm{y}_{1}, \mathrm{z}_{1}\right)$
and $Q\left(x_{2}, y_{2}, z_{2}\right)$ in the ratio $m: n$ are
$\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}, \frac{m z_{2}+n z_{1}}{m+n}\right)$
Point $A(2,1,-3)$ and $B(5,-8,3), m$ and $n$ are 2 and 1 respectively.
Using the above formula, we get,
$\left(\frac{2 \times 5+1 \times 2}{2+1}, \frac{2 \times-8+1 \times 1}{2+1}, \frac{2 \times 3+1 \times-3}{2+1}\right)$
$\left(\frac{12}{3}, \frac{-15}{3}, \frac{3}{3}\right)$
( 4,-5, 1), is the point of trisection of the segment AB.