Find the ratio in which the line joining the points `(1,2,3)a n d(-3,4,-5)` is divided by the `x y-p l a n e` . Also, find the coordinates of the point of division.

Explanation

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 = (−3k+1)/(k+1) ; y = (4k+2)/(k+1); z = (−5k+3)/(k+1)`
Since the point lies on xy-axis, we have; `z=0⇒(−5k+3)/(k+1) = 0 ⇒ -5k + 3 = 0 ⇒ k = 3/5 `
Thus the required ratio is` 3:5 ; ie, 3:5.`