# Direction of Pseudovectors

The Wikipedia article on http://en.wikipedia.org/wiki/Pseudovector" [Broken] initally suggests that they do change direction after reflection.

Geometrically it (a pseudovector) is the opposite, of equal magnitude but in the opposite direction, of its mirror image. This is as opposed to a true or polar vector (more formally, a contravariant vector), which on reflection matches its mirror image.

But in a later http://en.wikipedia.org/wiki/Pseudovector#Physical_examples" angular momentum remains invariant under reflection.

Each wheel of a car driving away from an observer has an angular momentum pseudovector pointing left. The same is true for the mirror image of the car.

A pseudovector is direction invariant under reflection or not?

I tried to devise a trick on the Right Hand Rule - if I were to switch to a left hand rule (left hand appears to be a mirror image of the right hand), and curl my left palm as in right hand rule. I noticed that if the left hand is to be maintained as a mirror image of the right, the direction of both the thumbs is same, suggesting that it is invariant.

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D H
Staff Emeritus
The Wikipedia article on http://en.wikipedia.org/wiki/Pseudovector" [Broken] initally suggests that they do change direction after reflection.
Geometrically it (a pseudovector) is the opposite, of equal magnitude but in the opposite direction, of its mirror image. This is as opposed to a true or polar vector (more formally, a contravariant vector), which on reflection matches its mirror image.
But in a later http://en.wikipedia.org/wiki/Pseudovector#Physical_examples" angular momentum remains invariant under reflection.

Well, that's wikipedia for ya'. Sometimes very good, sometimes poorly written and confusing, sometimes flat out wrong. This article falls in the second category.

Think of the car on the left as the real car, the car on the right as the car's reflection. Imagine a vector on the car's rear bumper, with the tail in the middle of the red/gray hatched region and the head in the middle of the red/blue hatched region. In the car on the left, this vector is parallel to the angular momentum vectors of the car's wheels. Upon reflection, this vector reverses direction: It is points to the right upon reflection. This displacement vector is a real vector rather than a pseudovector. It's reflected image is the reverse of the real image in this particular example. The angular momentum pseudovectors are reflected and reversed. Reflection alone would reverse the direction of the pseudovectors. Reversing the reflections of these pseudovectors leaves those pseudovectors unchanged in this particular example.

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Chandra Prayaga