Show that the vectors are coplanar, when

i. and


ii. and


iii. and


i. and


Given Vectors :





To Prove : Vectors are coplanar.


i.e.


Formulae :


1) Scalar Triple Product:


If





Then,



2) Determinant :



Answer :


For given vectors,







= 1(3) + 2(-6) + 3(3)


= 3 – 12 +9


= 0



Hence, the vectors are coplanar.


Note : For coplanar vectors ,



ii. and


Given Vectors :





To Prove : Vectors are coplanar.


i.e.


Formulae :


1) Scalar Triple Product:


If





Then,



2) Determinant :



Answer :


For given vectors,







= 1(4) – 3(6) + 1(14)


= 4 – 18 + 14


= 0



Hence, the vectors are coplanar.


Note : For coplanar vectors ,



iii. and


Given Vectors :





To Prove : Vectors are coplanar.


i.e.


Formulae :


1) Scalar Triple Product:


If





Then,



2) Determinant :



Answer :


For given vectors,







= 2(2) + 1(16) + 2(-10)


= 4 + 16 -20


= 0



Hence, the vectors are coplanar.


Note : For coplanar vectors ,



1