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

A=(3,4,1);B=(5,1,6)
The line can be written as r=(3,4,1)+t(2,-3,5)
This also can be written as
t = (x-3)/2 = (y-4)/-3 = (z-1)/5
Since we need the coordinates of the point where the line crosses the x-y plane, we make z equal to zero.
∴t=(0-1)/5=-1/5
∴(x-3)/2=-1/5 ⇒5x-15=-2 or x=13/5
Similarly,(y-4)/-3=-1/5 ⇒5y-20=3 or y=23/5
The coordinates thus become (13/5,23/5,0)