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