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 | u·v | scalar cross product | uxv | pseudovector perp dot product | u^⊥·v | scalar vector direct product | u v | tensor Vector multiplication can also be defined for vectors taken three at a time, as summarized in the following table.

cross product | dot product | perp dot product | scalar multiplication | scalar triple product | vector | vector addition | vector direct product | vector quadruple product | vector triple product