Question

If vector(a, b, c) are coplanar vectors, then show that |vector(a, b, c), vector(a.a, a.b, a.c), vector(b.a, b.b, b.c)| = vector 0

Answer 1

Since vactor(a, b, c) are coplanar there must exist k₁, k₂, k₃ not all zero (say k₁ ≠ 0) such that vactor(k₁a + k₂b + k₃c) = 0. Now by operating C₁→ k₁ C₁ + k₂C₂ + k₃C₃, we have