Show that the following points are collinear :
P(3, -2, 4), Q(1, 1, 1) and R(-1, 4, 2)
To prove: the 3 points are collinear.
Formula:
The distance between two points (x1,y1,z1) and (x2,y2,z2) is given by
D=
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 PQ= 
= 
= 
= 
= 
Length QR= 
= 
= 
= 
= 
Length PR = 
= 
= 
= 
= 
= 2
PQ + QR= 
+ 
=2 
= PR
Therefore P, Q, R are collinear.
1