Question

Find the coordinates of the point where the line through the points $A\left(3,4,1\right)$ and $B\left(5,1,6\right)$ crosses the $xy$ plane.

Answer 1

Equation of line is

$\frac{x-3}{3-5}=\frac{y-4}{4-1}=\frac{z-1}{1-6}$

$\frac{x-3}{-2}=\frac{y-4}{3}=\frac{z-1}{-5}$

In $xy$ plane $z=0$

$\frac{z-3}{-2}=\frac{y-4}{3}=\frac{1}{5}$

$x=\frac{-2}{5}+3=\frac{13}{5}$

$y=\frac{3}{5}+4=\frac{23}{5}$

Coordinate of point are $(\frac{13}{5},\frac{23}{5},0)$