In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. If a scalar is considered a degree zero quantity, and a vector is a degree one quantity, then a bivector can be thought of as being of degree two.

Is the cross product a bivector?

The vector cross gives a bivector rather than a vector. Its not very strange that the product of two vectors is not a vector itself, its the same principle as the dot product which produces a scalar. In fact the cross product and dot products are complimentary.

Is a bivector a tensor?

An antisymmetric tensor of second rank (a.k.a. 2-form).