Using distance formula prove that the following points are collinear :
A(3, -5, 1), B(-1, 0, 8) and C(7, -10, -6)
Given: A(3, -5, 1), B(-1, 0, 8) and C(7, -10, -6)
To prove: Points A, B and C are collinear
Formula used:
Points A, B and C are collinear if AB + BC = AC or AB + AC = BC or AC + BC = AB
Distance between any two points (a, b, c) and (m, n, o) is given by,
Therefore,
Distance between A(3, -5, 1) and B(-1, 0, 8) is AB,
Distance between B(-1, 0, 8) and C(7, -10, -6) is BC,
Distance between A(3, -5, 1) and C(7, -10, -6) is AC,
Clearly,
AB + AC
= BC
Hence, A, B and C are collinear