If the vectors and be coplanar, show that c² = ab.

Given : vectors are coplanar. Where,

To Prove : c² = ab

Formulae :

1) Scalar Triple Product:

If

Then,

2) Determinant :

Answer :

As vectors are coplanar

………eq(1)

For given vectors,

= a.(- c) – a.(b - c) + c(c)

= – ac – ab + ac + c²

= - ab + c²

………eq(2)

From eq(1) and eq(2),

- ab + c² = 0

Therefore,

Hence proved.

Note : Three vectors are coplanar if and only if