Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Let point $P(x,y,z)$ divides the line joining the points $A$ and $B$ in the ratio $m:1$.
Since, point $P$ is on $XOZ$ -plane $\therefore y$ coordinate $=0$ $\Rightarrow \frac{2m-3}{m+1}=0$ $\Rightarrow m=\frac{3}{2}$ Now, $x=\frac{3+2\times 5}{3+2}=\frac{13}{5}$ and $z=\frac{3\times (-2)+2\times (-2)}{5}=-2$ $\therefore$ Required point is $\left(\frac{13}{5},0,-2\right)$.