Scalar triple product ↩

shorthands: {}
aliases: [Mixed product, mixed product, box product, Box product, triple scalar product, Triple scalar product]
created: 2021-10-20 10:12:28
modified: 2022-01-10 04:13:04

is the (signed) volume of the parallelepiped defined by the three vectors given.
In Einstein notation:

Properties

• Invariant to cyclic premutations of the vectors (easy to see from the Einstein notation form):
• Invariant to swapping the positions of the operators:
• Swapping any two vectors negates the product
• If the product is , the vectors are coplanar
• Can be expressed as a determinant: