A trivector is an oriented segment of a 3 dimensional manifold. Just as a vector has a magnitude and a direction so a trivector has a magnitude corresponding to its area and an orientation. In three dimensions a trivectors has only one possible orientation therefore in three dimensions a trivector is a pseudoscalar. In three dimensions the dual of a trivector is a scalar. (In four dimensions a trivector is a pseudovector)

A∧B∧C = Trivector whose magnitude is equal to the area of the parallelepiped swept out by vectors A, B, and C.