Question -
Answer -
(i) A(4,-3, -1), B(5, -7, 6) and C(3, 1, -8)
Given:
The points A(4, -3, -1), B(5, -7, 6) and C(3, 1, -8)
Points A, B and C are collinear if AB + BC = AC or AB + AC = BCor AC + BC = AB
By using the formula,
The distance between any two points (a, b, c) and (m, n, o)is given by,
∴Thepoints A, B and C are collinear.
(ii) P (0,7, -7), Q (1, 4, -5) and R (-1, 10, -9)
Given:
The points P (0, 7, -7), Q (1, 4, -5) and R (-1, 10, -9)
Points P, Q and R are collinear if PQ + QR = PR or PQ + PR = QRor PR + QR = PQ
By using the formula,
Distance between any two points (a, b, c) and (m, n, o) is givenby,
∴Thepoints P, Q and R are collinear.
(iii) A(3,-5, 1), B(-1, 0, 8) and C(7, -10, -6)
Given:
The points A(3, -5, 1), B(-1, 0, 8) and C(7, -10, -6)
Points A, B and C are collinear if AB + BC = AC or AB + AC = BCor AC + BC = AB
By using the formula,
The distance between any two points (a, b, c) and (m, n, o)is given by,
∴Thepoints A, B and C are collinear.