Answer :

Given: Points are P(0, 1, 2), Q(4, -2, 1) and O(0, 0, 0)


To check: the value of POQ


Formula used:


Distance between any two points (a, b, c) and (m, n, o) is given by,



Therefore,


Distance between P(0, 1, 2) and Q(4, -2, 1) is PQ,






Distance between Q(4, -2, 1) and O(0, 0, 0) is QO,






Distance between P(0, 1, 2) and O(0, 0, 0) is PO,






Now,


PO2 = 5


QO2 = 21


PQ2 = 26


Clearly,


PO2 + QO2 = PQ2


A right-angled triangle is a triangle which satisfies Pythagoras Theorem


These points satisfy Pythagoras Theorem


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