Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the ZX-plane.

Explanation

We know that the equation of ZX-plane is `y = 0`
Equation of a line passing through the points `(5,1,6)` and (3,4,1).
`(x-5)/(3-5) = (y-1)/(4-1) = (z-6)/(1-6)`
`rArr (x-5)/(-2) = (y-1)/(3) = (z-6)/(-5) = lambda` (say)
Let any point on this line is
`(5-2lambda, 1+3lambda, 6-5lambda)"........"`
This line passes through zx-plane.
`:.` From equation (1), `1+3lambda= 0 rArr lambda = - 1/3 "....."(2)`
Point of intersection of equations (1) and (2) is
`(5+(2)/(3),0,6+(5)/(3)) = (17/3,0,29/3)`