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Cross Product

  1. Jan 31, 2013 #1
    What is the cross product of a constant and a vector? I know that the cross product between two vectors is the area of the parallelogram those two vectors form. My intuition tells me that since a constant is not a vector, it would only be multiplying with a vector when in a cross product with one. Since the vector will only grow larger in magnitude, there would be zero area in the paralleogram formed because there is no paralleogram.
     
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  3. Jan 31, 2013 #2

    micromass

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    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.

     
  4. Jan 31, 2013 #3
    So if I had an equation that contains a term that has a cross product of a constant and a vector, do I just cross it out of the equation? ( it is in an adding term so crossing it out would be okay). That's an awesome joke(:
     
  5. Jan 31, 2013 #4

    micromass

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    Can you give a specific example?
     
  6. Jan 31, 2013 #5
    Sure! An equation like F=π[hXh+cXh] where h is a vector and c is a constant.
     
    Last edited: Jan 31, 2013
  7. Jan 31, 2013 #6

    micromass

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    That doesn't really make any sense.
     
  8. Jan 31, 2013 #7
    F is a vector.
     
  9. Jan 31, 2013 #8
    F=π[hXh+cXh] Sorry about not adding the equality.
     
  10. Jan 31, 2013 #9
    Would the term containing the cross product of the constant c and vector h in the above equation just be zero? Or am I able to take cross it out of the above equation?
     
  11. Jan 31, 2013 #10

    micromass

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    No. As it stands, your equation makes no sense. You can't take the cross product of a scalar and a vector.
     
  12. Jan 31, 2013 #11
    Damn that stinks. Even if the c was a constant?
     
  13. Jan 31, 2013 #12

    micromass

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    Does this equation appear in some book or anything? Can you provide some more context?
     
  14. Jan 31, 2013 #13
    Well I made it up haha. Im sorry. I'm new at this. Do you think you can make an equation that makes sense? Like the one I attempted but failed at.
     
  15. Jan 31, 2013 #14

    micromass

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    It only makes sense if you take the cross of a vector and a vector.

    What were you attempting to do?? What lead you to this particular equation?
     
  16. Jan 31, 2013 #15
    Well, the h is a vector that represents a magnetic field strength. In the definition of a current, I=dq/dt, multiplying both sides by a small length ds would give the magnetic field produced my a moving charge. (dq/dt)ds turns into dq(ds/dt) which turns into vdq where dq is a small piece of charge and v is the velocity of the total charge. Integrating both sides to I ds=vdq would give the total magnetic field. For a constant velocity, the right side of the above equation turns into vq+ c, where c is some constant. Now I get the equation h=vq+c. Solving for qv gives me h-c=qv. In the equation for magnetic force on a moving charge, F=qvxB. I substituted h-c for qv in the above force equation. B turns into uh where u is the permeability of free space. I substitute uh for B in the magnetic force equation and get F=u[hxh-cxh]. I want the cxh term to go away.
     
  17. Jan 31, 2013 #16
    Does that sort of help?
     
  18. Jan 31, 2013 #17

    micromass

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    I don't understand any of what you said, but my physics is very bad. I'll move this to the physics section for you.
     
  19. Jan 31, 2013 #18
    Thank you very much!(:
     
  20. Jan 31, 2013 #19

    HallsofIvy

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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.
     
  21. Jan 31, 2013 #20
    Ohhh. That makes a lot of sense! Is there anyway I could determine what the constant vector is?
     
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