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Thread: Solving a simple crossproduct expression

  1. #1 Solving a simple crossproduct expression 
    Forum Freshman jmd_dk's Avatar
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    Hey. I'm stuck with this annoying problem. Sure, there must be a solution. I just can't find it

    Let c be the cross product of a with b, which both are 3-dimensional vectors:
    c = a x b

    Now, how do we solve for either a or b?

    /Thanks


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  3. #2  
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    impossible, because they are not determined by that expression. It is possible to find the plane in which a and b lie (perpendicular to c), and if e.g. a is given, you can find a relation between angle and magnitude for b, but you can't determine b entirely.


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  4. #3  
    Forum Freshman jmd_dk's Avatar
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    Seriously? Aww...

    I have this situation:


    It's physics, but the problem is purely mathematical, really. I know the formula for v:
    v = r x omega. If i want to express omega (as a vector) in terms of v and r, that's impossible, you say?
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  5. #4  
    Forum Radioactive Isotope MagiMaster's Avatar
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    I don't have time to work through this very thoroughly, but I think that if you know v and r are at right angles, then w is either vxr or rxv (not sure which off the top of my head). Otherwise you get a curve of possible answers (maybe a line) for w.
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  6. #5  
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    ... if v is perpendicular to r, the cross product of them is 0 iirc
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

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  7. #6  
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    Quote Originally Posted by Arcane_Mathematician
    ... if v is perpendicular to r, the cross product of them is 0 iirc
    That's the dot product. The cross product is 0 if the vectors are parallel.

    To solve the problem, you need some extra information, such as the direction of .
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  8. #7  
    Forum Professor wallaby's Avatar
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    Looking at the diagram i figure that since they've shown that the vectors r and v are perpendicular, while neglecting to show that the same occurs for omega and r, then it would be best to assume that the two vectors are separated by an angle theta. Now that you know why i'm including the angle between the vectors...

    I believe you can find what you're looking for by using the following definition of the cross product.

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