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ZixuanZhang
ZixuanZhang
Ponder...

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