Find the value of λ for which the vectors are coplanar, when

i. and

ii. and

iii. and

i. .. and

Given : Vectors are coplanar.

Where,

To Find : value of

Formulae :

1) Scalar Triple Product:

If

Then,

2) Determinant :

Answer :

As vectors are coplanar

…………eq(1)

For given vectors,

…………eq(2)

From eq(1) and eq(2),

ii. and

Given : Vectors are coplanar.

Where,

To Find : value of

Formulae :

1) Scalar Triple Product:

If

Then,

2) Determinant :

Answer :

As vectors are coplanar

…………eq(1)

For given vectors,

…………eq(2)

From eq(1) and eq(2),

iii. .. and

Given : Vectors are coplanar.

Where,

To Find : value of

Formulae :

1) Scalar Triple Product:

If

Then,

2) Determinant :

Answer :

As vectors are coplanar

…………eq(1)

For given vectors,

…………eq(2)

From eq(1) and eq(2),