Question

Show that the following points are collinear : 

A(-2, 3, 5), B(1, 2, 3) and C(7, 0, -1)

Answer 1

To prove: the 3 points are collinear. 

Formula: The distance between two points (x₁,y₁,z₁) and (x₂,y₂,z₂) is given by

D = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\)

Here, 

(x₁,y₁,z₁) = (-2, 3, 5) 

(x₂,y₂,z₂) = (1, 2, 3) 

(x₃,y₃,z₃) = (7, 0, -1)

Length AB = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\)

 Length AC = \(\sqrt{(x_3-x_1)^2+(y_3-y_1)^2+(z_3-z_1)^2}\)

Therefore A, B, C are collinear.