Q. 9

# If the vectors and be coplanar, show that c^{2} = ab.

Answer :

Given : vectors are coplanar. Where,

To Prove : c^{2} = 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 + c^{2}

= - ab + c^{2}

………eq(2)

From eq(1) and eq(2),

- ab + c^{2} = 0

Therefore,

Hence proved.

Note : Three vectors are coplanar if and only if

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