Scalaire en vector drievoudige producten

The scalar triple product is the dot product of a vector with the cross product of two vectors. It results in a scalar quantity.

Here, the magnitude of the cross product of two vectors gives the area of the parallelogram formed by these vectors. The resultant vector is perpendicular to the parallelogram plane.

The projection of the third vector in the direction of the resultant of the cross product gives the height of the parallelepiped.

It follows that the resultant of the scalar triple product denotes the volume of the parallelopiped formed by these vectors.

The volume remains unaltered if the vectors are rotated in cyclic order in the scalar triple product.

The Vector triple product is the cross product of a vector with the resultant of the cross product of two vectors and results in a vector quantity.

Here, if the vectors are rotated in cyclic order, the resultant vector is entirely new. So, the vector triple product is not associative.