Find the ratio in which the line segment joining the points (1, 3, 5) and (-4, 3, -6) is divided by
the XY-plane. Also, find the coordinates of the point of division.

Explanation

Let the join of the line segment A(1, 3, 5) and B(-4, 3, -6) be divided by the XY-plane at a point
P in k : 1 Then the coordinates of P are given by

`((-4k+1)/(k+1), (3k+3)/(k+1), (-6k+5)/(k+1)) ...(i)`
Now, P lies on XY-plane i.e. , z = 0
`therefore (-6k+5)/(k+1)=0 rArr k =5/6`
So, the required ratio is 5 : 6
On putting `k= 5/6 in (i)` we get the coordinates of P as `((_14)/11,3, 0)`.