Scalar triple product
is invariant under cyclic permutation and equals the signed volume of the parallelepiped formed by the three vectors.
Cyclic properties
Proposition 2.23
For , we have
Signed volume
is a signed volume: it is positive when constitute a right-handed set, and zero iff the three vectors are coplanar, that is, one is a linear combination of the other two. In , the analogous bracket gives the signed area of the parallelogram formed by and .
Related
Stated in
- Definition 2.22 (Scalar Triple Product)§2.5.1 Scalar Triple Product
- Proposition 2.23§2.5.1 Scalar Triple Product
