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 ,