Question

Using vector method, show that the given points A, B, C are collinear: A(3, −5, 1), B(−1, 0, 8) and C(7, −10, −6)

Answer 1

Through the vertices we get the adjacent vectors as,

\(\overset{\rightarrow}{AB}\) = -4i+5j+7k and \(\overset{\rightarrow}{AC}\) = 4i - 5j - 7k

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