  The cross product frequently occurs in Physics and Engineering, since it has
large applications in many contexts, e.g. for calculating angular momenta,
torques, rotations, volumes etc. Though this mathematical operator is widely
used, it is commonly expressed in a 3-D notation which gives rise to many
paradoxes and difficulties. In fact, instead of other vector operators like
scalar product, the cross product is defined just in 3-D space, it does not
respect reflection rules and invokes the concept of "handedness". In this paper
we are going to present an extension of cross product in an arbitrary number N
of spatial Dimensions, different from the one adopted in the Exterior Algebra
and explicitly designed for an easy calculus of moments.
