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 ,