Question

Find the ratio in which the line segment joining the points $(4,8,10)$ and $(6,10,-8)$ is divided by $YZ-$ Plane.

Answer 1

Let the point of intersection on $yz$ plane be $(0,y,z)$

By section formula, $x=\left(\frac{m{x}_2+n{x}_1}{m+n}\right)$ where $m:n=k:1$

$\Rightarrow 0=\frac{6k+4}{k+1}\Rightarrow k=-\frac{4}{6}=-\frac{2}{3}$

Therefore, line is divide in ration $2:3$ externally