Answer :

If three points are collinear, then they lie on a line.


Let first calculate distance between the 3 points


i.e. PQ, QR and PR


Calculating PQ


P ≡ (– 2, 3, 5) and Q ≡ (1, 2, 3)


Distance PQ


Here,


x1 = – 2, y1 = 3, z1 = 5


x2 = 1, y2 = 2, z2 = 3


Distance PQ





Calculating QR


Q ≡ (1, 2, 3) and R ≡ (7, 0, – 1)


Distance QR


Here,


x1 = 1, y1 = 2, z1 = 3


x2 = 7, y2 = 0, z2 = – 1


Distance QR






Calculating PR


P ≡ (– 2, 3, 5) and R ≡ (7, 0, – 1)


Distance PR


Here,


x1 = – 2, y1 = 3, z1 = 5


x2 = 7, y2 = 0, z2 = – 1


Distance PR






Thus, PQ = , QR = & PR =


So, PQ + QR = + = = PR


Thus, Points P, Q and R are collinear.


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