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.

Explanation

The equation of the line through the points A(3,4,1) and B(5,1,6) is given by
`(x-3)/(5-3)=(y-4)/(1-4)=(z-1)/(6-1) rArr (x-3)/2=(y-4)/-3=(z-1)/5`………..(i)
the equation of the XY-plane is z=0.
Since the line (i) meets the XY-plane, we have
`(x-3)/(2)=(y-4)/-3 = (0-1)/5 rArr (x-3)/2=-1/5` and `(y-4)/-3=-1/5`
`rArr x=(3-2/5)=13/5,y=(4+3/5)=23/5` and `z=0`.
Hence, the given line crosses the XY-plane at the point
`P(13/5,23/5,0)`.