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 | pseudoscalar |
A number of vector quadruple products can also be defined.