- #1

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[tex]\vec{r} = \left( \begin{array}{ccc}c*t & x & y & z \end{array} \right)[/tex]

[tex]\vec{v} = \left( \begin{array}{ccc}c & vx & vy & vz \end{array} \right)[/tex]

[tex]\vec{v} \times \vec{r} = ?[/tex]

[tex][/tex]

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- Thread starter Philosophaie
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- #1

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[tex]\vec{r} = \left( \begin{array}{ccc}c*t & x & y & z \end{array} \right)[/tex]

[tex]\vec{v} = \left( \begin{array}{ccc}c & vx & vy & vz \end{array} \right)[/tex]

[tex]\vec{v} \times \vec{r} = ?[/tex]

[tex][/tex]

- #2

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See http://en.wikipedia.org/wiki/Cross_product#Cross_product_as_an_exterior_product

What is the purpose of your proposed construction?

- #3

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Actually it's also well defined non-trivially for 7 dimensions.

- #4

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The triple product is:[tex]v \times r = \bar{x}*(vy*z-vz*y) + \bar{y}*(vz*x-vx*z) + \bar{z}*(vx*y-vy*x)[/tex]

- #5

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Still not clear what you are trying to accomplish with the 4-vectors here.

- #6

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If you give the context under which you want to ask this kind of question, we can probably identify what you actually want to do with your two vectors.

- #7

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- #8

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[tex]\vec{v} \times \vec{r} = 2*(v_z*c*t-c*z)*\bar{x}\bar{y}+2*(v_y*c*t-c*y)*\bar{x}\bar{z}+2*(v_x*c*t-c*x)*\bar{y}\bar{z}+2*\bar{t}*(\bar{x}*(v_x*y-y-v_y*x)+\bar{y}*(v_z*x-v_x*z)+\bar{z}*(v_x*y-v_y*x))[/tex]

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- #11

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