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),





1