A line through the points A(3, 4, 1) and B(5, 1, 6) is drawn.

The coordinates of the points where the line through the points A & B crosses the XY plane is :

$\left(\frac{13}{5},\frac{23}{5},0\right)$

line AB: $\frac{(x-3)}{5-3}=\frac{y-4}{1-4}=\frac{z-1}{6-1}⇒\frac{x-3}{2}=\frac{y-4}{-3}=\frac{z-1}{5}$

in (x, y) plane z = 0

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

$x=2(\frac{3}{2}-\frac{1}{5}),y=4+\frac{3}{5}$

so $(x,y,z)=\left(\frac{13}{5},\frac{23}{5},0\right)$