Answer :

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.


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