Q. 9

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

Answer :

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



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