Question

Show that the point A, B, C with position vectors (3i - 2j + 4k), (i + j + k) and (-i + 4j - 2k) respectively are collinear.

Answer 1

Through the vertices we get the adjacent vectors as,

\(\overset{\rightarrow}{AB}\) = -2i + 3j - 3k and \(\overset{\rightarrow}{AC}\) = -4i + 6j - 6k

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.