The xy-plane divides the line joining the points (-1, 3, 4) and (2, -5, 6)

externally in the ratio 2 : 3

Suppose xy-plane divides the line joining the given points in the ratio λ : 1. The coordinates of the point of division are $\left(\frac{2λ-1}{λ+1}, \frac{-5λ+3}{λ+1}, \frac{6λ+4}{λ+1}\right).$

This point lies on xy-plane,

$∴\frac{6λ+4}{λ+1}= 0 ⇒ λ =-\frac{2}{3}$

Hence, xy-planes divided externally in the ratio 2 : 3.