Given: A(2, -3, 4), B(-1, 2, 1) and

To prove: A, B and C are collinear

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 divides AB in ratio k: 1

Three points are collinear if the value of k is the same for x, y and z coordinates

Therefore, m = k and n = 1

A(2, -3, 4), B(-1, 2, 1) and

Coordinates of C using section formula:

On comparing:

⇒ 2 = -1(k + 1)

⇒ 2 = -k – 1

⇒ k = -1 – 2

⇒ k = -3

⇒ k – 9 = 6(k + 1)

⇒ k – 9 = 6k + 6

⇒ k – 6k = 6 + 9

⇒ -5k = 15

⇒ k = -3

⇒ 2k + 4 = 1(k + 1)

⇒ 2k + 4 = k + 1

⇒ 2k – k = 1 – 4

⇒ k = -3

The value of k is the same in all three times

Hence, A, B and C are collinear