Question

Find the ratio in which the line segment having the end points A(-1, -3, 4) and B(4, 2, -1) is divided by the xz-plane. Also, find the coordinates of the point of division.

Answer 1

Let the plane XZ divides the points A(-1, -3, 4) and B(4, 2, -1) in ratio k:1.

Using section formula, we have

Since we are given with xz-plane, so y-coordinate is zero here.

Choosing y-coordinate, we have

0 = (2k-3)/(k+1)

or k = 3/2

The ratio is 3:2 in XZ plane which divides AB.