Find the coordinates of the point which divides the join

The coordinates of point R that divides the line segment joining points P $(\mathrm{X} 1 $\left.\mathrm{y}_{1}, \mathrm{z}_{1}\right)$

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( 3, 2, 5 ) and B( -4, 2, -2 ), m and n are 4 and 3 respectively.

Using the above formula, we get,

$=\left(\frac{4 \times-4+3 \times 3}{4+3}, \frac{4 \times 2+3 \times 2}{4+3}, \frac{4 \times-2+3 \times 5}{4+3}\right)$

$=\left(\frac{-7}{7}, \frac{14}{7}, \frac{7}{7}\right)$

$(-1,2,1)$, is the point which divides the two points in ratio $4: 3$.