Question

Show that the points having position vectors a, b, (c = 3a - 2b) are collinear, whatever be a, b, c.

Answer 1

Through the vertices we get the adjacent vectors as,

\(\overset{\rightarrow}{AB}\) = b - a and \(\overset{\rightarrow}{AC}\) = c - a = 2a + 2b

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.