Question

Using vector method, show that the given points A, B, C are collinear: A(6, −7, −1), B(2, −3, 1) and C(4, −5, 0).

Answer 1

Through the vertices we get the adjacent vectors as,

\(\overset{\rightarrow}{AB}\) = -4i+4j+2k and \(\overset{\rightarrow}{AC}\) = -2i+2j+k

To prove that A, B, C are collinear we need to prove that

Thus, substituting the values of a₁, a₂, a₃ and b₁, b₂ and b₃, in equation (i) we get

Thus, A, B and C are collinear.