Let the line joining the points A(1, 2, 3) and B(-3, 4, -5) is divided by the xy-plane in the ratio k:1.
Then the coordinate
x = \(\frac{-3k + 1}{k+1}\); y = \(\frac{4k + 2}{k+1}\); z = \(\frac{-5k+3}{k+1}\)
Since the point lies on xy-axis, we have;
\(z = 0 \Rightarrow \frac{-5k+3}{k+1}\) = 0 \(\Rightarrow
\) -5k + 3 = 0 \(\Rightarrow\) k = \(\frac{3}{5}\)
Thus the required ratio is \(\frac{3}{5}\); ie, 3:5.
