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.



1