Editing Cross product (section)

=== Exterior product ===
{{Main|Exterior algebra|Comparison of vector algebra and geometric algebra#Cross and exterior products}}
In general dimension, there is no direct analogue of the binary cross product that yields specifically a vector. There is however the exterior product, which has similar properties, except that the exterior product of two vectors is now a [[p-vector|2-vector]] instead of an ordinary vector. As mentioned above, the cross product can be interpreted as the exterior product in three dimensions by using the [[Hodge star]] operator to map 2-vectors to vectors.  The Hodge dual of the exterior product yields an {{nowrap|(''n'' − 2)}}-vector, which is a natural generalization of the cross product in any number of dimensions.

The exterior product and dot product can be combined (through summation) to form the [[Geometric algebra|geometric product]] in geometric algebra.