Question

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.

Answer 1

Here, we are given points `A(3,4,1)` and `B(5,1,6)`.
So, direction ratio of line `AB = (2,-3,5)`.
So, equation of line becomes,
`(x-3)/2 = (y-4)/-3 = (z-1)/5 = k`
`=>(z-1)/5 = k`
As the line is crossing XY-plane, z-coordinate will be `0`. So, `(0-1)/5 = k => k = -1/5`
`:. (x-3)/2 = -1/5 => x = 3-2/5 = 13/5`
`(y-4)/-3 = -1/5 => y = 4+3/5 = 23/5`
So, the required coordinates will be `(13/5,23/5,0)`.