Given :
Let A, B, C & D be four points with position vectors a, b, c and d.
Therefore,
To Prove : Points A, B, C & D are coplanar.
Formulae :
1) Vectors :
If A & B are two points with position vectors a and b,
Where,
then vector AB is given by,
2) Scalar Triple Product:
If
Answer :
For given position vectors,
Vectors BA, CA and DA are given by,
Now, for vectors
Hence, vectors BA, CA and DA are coplanar.
Therefore, points A, B, C & D are coplanar.
Note : Four points A, B, C & D are coplanar if and only if [BA CA DA] = 0
