Given Vectors :

To Prove : Vectors are parallel to same plane.

Formulae :

1) Scalar Triple Product:

If

Then,

2) Determinant :

Answer :

Vectors will be parallel to the same plane if they are coplanar.

For vectors to be coplanar,

Now, for given vectors,

= 1(4) – 3(6) + 1(14)

= 4 – 18 + 14

= 0

Hence, given vectors are parallel to the same plane.