Show that the following points are collinear :
A(-2, 3, 5), B(1, 2, 3) and C(7, 0, -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=
Here,
(x1,y1,z1)= (-2, 3, 5)
(x2,y2,z2)= (1, 2, 3)
(x3,y3,z3)= (7, 0, -1)
Length AB = 
= 
= 
= 
= 
Length BC = 
= 
= 
= 
= 
= 2
Length AC = 
= 
= 
= 
= 
= 3
AB + BC = 
+ 2 
=3 
= AC
Therefore A, B, C are collinear.
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