# Find the ratio in

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

5k + 5 = 4

5k = 4 – 5

5k = – 1 Hence, the plane divides AB externally in ratio 1:5

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