Cross Product

quantumfoam

Thank you very much!(:

HallsofIvy

Saying that c is a 'constant' doesn't mean it is not a vector. A "constant" is simply something that does not change as some variable, perhaps time or a space variable, changes. In your formua c is a constant vector.

quantumfoam

Ohhh. That makes a lot of sense! Is there anyway I could determine what the constant vector is?

sankalpmittal

A constant vector does not have to be a scalar !! A constant vector has a constant magnitude and a constant direction...

stevendaryl

On the other hand, there is a generalization, the exterior product. The exterior product of a scalar and a vector is a vector. The exterior product of two vectors is a bivector. The exterior product of a vector with a bivector is a trivector. Etc.

In 3D, there are three independent bivectors: [itex]B_{xy}, B_{yz}, B_{zx}[/itex]. The cross product can be thought of as the exterior product, combined with the identification of [itex]B_{xy}[/itex] with the unit vector [itex]\hat{z}[/itex], [itex]B_{yz}[/itex] with the unit vector [itex]\hat{x}[/itex], and [itex]B_{zx}[/itex] with the unit vector [itex]\hat{y}[/itex].

Considering the result of the exterior product of two vectors to be another vector only works in 3D. In 2D, the exterior product of two vectors is a pseudo-scalar.