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What is the difference between an axial vector, a psudo vector and a bivector?

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- Thread starter Swapnil
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- #1

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What is the difference between an axial vector, a psudo vector and a bivector?

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Hurkyl

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Axial vector and pseudo-vector seem to mean the same thing, and are dual to bivectors.

A bivector is a "directed area". (similar to how a vector is a "directed length") In three dimensions, a directed area can be represented by its normal vector (i.e. it's "axis"): that's where pseudovectors come from.

Similarly, in three dimensions, a "directed volume" can be represented by a number: that's where pseudoscalars come from.

A bivector is a "directed area". (similar to how a vector is a "directed length") In three dimensions, a directed area can be represented by its normal vector (i.e. it's "axis"): that's where pseudovectors come from.

Similarly, in three dimensions, a "directed volume" can be represented by a number: that's where pseudoscalars come from.

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- #3

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[tex] \vec{C} = \vec{A}\times\vec{B}[/tex]

then

- #4

Hurkyl

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[itex]A \times B[/itex] is merely the properly oriented vector that is perpendicular to the oriented parallelogram with sides

(But only roughly speaking -- the picture isn't quite that nice. For example, [itex](A + B) \wedge B = A \wedge B[/itex])

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