The ratio on which the line joining the points (1, 2, 3) and (-3, 4, -5) is divided by xy-plane is

3 : 5 internally

Suppose the line joining the points P(1, 2, 3) and Q(-3, 4, -5) is divided the xy-plane at a point R in the ratio λ : 1. Then, the coordinates of R are

$\left(\frac{-3λ+1}{λ+1}, \frac{4λ+2}{λ+1}, \frac{-5λ+3}{λ+1}\right)$ ............(i)

Since R lies on xy-plane i.e.  z = 0

$∴ \frac{-5λ+3}{λ+1} = 0 ⇒ λ =\frac{3}{5}$

So, the required ratio is $\frac{3}{5} : 1 $ or, 3 : 5 internally.