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Calcmathlete

  • 3 years ago

How would you do the cross product of a two-dimensional vector? I've done three-dimensional ones, but not two-dimensional ones.

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  1. oldrin.bataku
    • 3 years ago
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    The cross product is not defined in R^2.

  2. Calcmathlete
    • 3 years ago
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    Then would I just say that there is no cross product?

  3. oldrin.bataku
    • 3 years ago
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    Sorta -- the cross product is not even applicable :-) ... unless you want a three-dimensional cross product, in which case you mean the vectors have an implicit zero component, e.g. \[u=ai+bj+0k\\ v = ci + dj + 0k\] You can find the three-dimensional cross product, which makes sense -- it's merely the surface normal to the plane defined.\[u \times v = (ad - bc)k\]

  4. Calcmathlete
    • 3 years ago
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    Oh ok. So if I were to have this problem, (the actual problem), let vector a = < 1, 2 > and vector b = < 3, 4 >. FInd the magnitude of vector c if vector c = vector a x vector b. Would it 2?

  5. oldrin.bataku
    • 3 years ago
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    It is wholly dependent on whether it expects you to do it in R^3 -- if not, then the question is silly because the cross product is not defined for R^2.

  6. Calcmathlete
    • 3 years ago
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    Ok...thank you...

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