TOPICS
Vector Multiplication
Although the multiplication of one vector by another is not uniquely defined (cf. scalar multiplication, which is multiplication of a vector by a scalar), several types of useful vector products can be defined, as summarized in the following table.
| product name | symbol | result |
| dot product |  | scalar |
| cross product |  | pseudovector |
| perp dot product |  | scalar |
| vector direct product |  | tensor |
Vector multiplication can also be defined for vectors taken three at a time, as summarized in the following table.
| product name | symbol | result |
| vector triple product |  | vector |
| scalar triple product | ![[u,v,w]](https://mathworld.wolfram.com/images/equations/VectorMultiplication/Inline6.svg) | pseudoscalar |
A number of vector quadruple products can also be defined.
See also
Cross Product, Dot Product, Perp Dot Product, Scalar Multiplication, Scalar Triple Product, Vector, Vector Addition, Vector Direct Product, Vector Quadruple Product, Vector Triple ProductExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Vector Multiplication." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/VectorMultiplication.html