A vector that does not reverse its sign when the coordinate system is changed to a new system by a reflection in the origin (i.e. $x_{\text{i}}^{\prime }=-x_{\text{i}}$). An example of an axial vector is the vector product of two polar vectors, such as L  =r  ×  p, where L is the angular momentum of a particle, r is its position vector, and p is its momentum vector. Compare pseudo-scalar.