Given: points A(2, 3, 1) and B(6, 7, 1)

To find: the ratio in which the line joining given points is divided by the XOZ-plane

Formula used:

Section Formula:

A line AB is divided by C in m:n where A(x, y, z) and B(a, b, c).

The coordinates of C is given by,

the y coordinate is always 0 on XOZ-plane

Let Point C(x, 0, z), and C divides AB in ratio k: 1

Therefore, m = k and n = 1

A(2, 3, 1) and B(6, 7, 1)

Coordinates of C using section formula:

On comparing:

⇒ 7k + 3 = 0(k + 1)

⇒ 7k + 3 = 0

⇒ 7k = –3

Hence, C divides AB externally in ratio 3: 7