Given: P(0, 7, -7), Q(1, 4, -5) and R(-1, 10, -9)

To prove: Points P, Q and R are collinear

Formula used:

Points P, Q and R are collinear if PQ + QR = PR or PQ + PR = QR or PR + QR = PQ

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

Therefore,

Distance between P(0, 7, -7) and Q(1, 4, -5) is PQ,

Distance between Q(1, 4, -5) and R(-1, 10, -9) is QR,

Distance between P(0, 7, -7) and R(-1, 10, -9) is PR,

Clearly,

PQ + PR

= QR

Hence, P, Q and R are collinear