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]](/images/equations/VectorMultiplication/Inline6.svg) | pseudoscalar |
A number of vector quadruple products can also be defined.
