Question

Show that the following points are collinear : 

P(3, -2, 4), Q(1, 1, 1) and R(-1, 4, 2)

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, Vertices should be R(-1, 4, -2) 

The solution according is 

(x₁,y₁,z₁) = (3, -2, 4) 

(x₂,y₂,z₂) = (1, 1, 1) 

(x₃,y₃,z₃) = (-1, 4,- 2)

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

Therefore P,Q,R are collinear