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Cross Product

by quantumfoam
Tags: cross, product
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HallsofIvy
#19
Jan31-13, 07:35 PM
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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
#20
Jan31-13, 07:44 PM
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Ohhh. That makes a lot of sense! Is there anyway I could determine what the constant vector is?
sankalpmittal
#21
Feb2-13, 01:33 AM
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Quote Quote by quantumfoam View Post
Ohhh. That makes a lot of sense! Is there anyway I could determine what the constant vector is?
A constant vector does not have to be a scalar !! A constant vector has a constant magnitude and a constant direction...
stevendaryl
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Feb2-13, 08:49 AM
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Quote Quote by micromass View Post
The cross product is only defined between vectors of [itex]\mathbb{R}^3[/itex]. The cross of a constant and a vector is not defined.
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.


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