Like the dot product, it depends on the metric of Euclidean space, but unlike the dot product, it also depends on a choice of orientation or "handedness". The product can be generalized in various ways; it can be made independent of orientation by changing the result to a pseudovector, or the exterior product of vectors can be used in arbitrary dimensions with a bivector or 2-form result. Also, using the orientation and metric structure just as for the traditional 3-dimensional cross product, one can, in dimensions, take the product of vectors to produce a vector perpendicular to all of them. But if the product is limited to non-trivial binary products with vector results, it exists only in three and seven dimensions. (See § Generalizations, below, for other dimensions.)