Polar versus Axial Vectors

show right-hand rule for axial vector
reflect in plane parallel to vectors
reflect in plane perpendicular to vectors

This Demonstration shows a polar vector, denoted by a straight line arrow, and an axial vector, denoted by three rotating arrows, with an option to use an arrow via the right-hand rule. These objects are not, in general, interchangeable. This Demonstration shows why—they behave differently under reflection and inversion.

• Reflection across a plane parallel to the vectors keeps the direction of a polar vector and reverses the direction of an axial vector.

• Reflection across a plane perpendicular to the vectors reverses the direction of a polar vector while keeping the direction of an axial vector.

• Inversion reverses the direction of a polar vector, but leaves an axial vector invariant.