Find the ratio in which the line segment joining the points (2, -1, 3) and (-1, 2, 1) is divided by the plane x + y + z = 5.

Given: A(2, -1, 3) and B(-1, 2, 1)

To find: the ratio in which the line segment AB is divided by the plane x + y + z = 5

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,

Let C(x, y, z) be any point on the given plane and C divides AB in ratio k: 1

Therefore, m = k and n = 1

A(2, -1, 3) and B(-1, 2, 1)

Coordinates of C using section formula:

On comparing:

Since, x + y + z = 5

⇒ 5(k + 1) = 4 + 2k

⇒ 5k + 5 = 4 + 2k

⇒ 5k – 2k = 4 – 5

⇒ 3k = – 1

Hence, the plane divides AB externally in ratio 1:3.