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Homework Help: Quick cross product question

  1. Apr 9, 2012 #1
    this is a general question - the thing i'm working on if what i am asking makes sense - i am currently only looking for a confirmation on what i think is right

    this is a vector product question:

    if i have:

    (A/c x cB)

    can i look at that as:

    (1/c*c)(A x B)

    which comes to

    A x B

    the question is - can i take the constant, c, out in the way i am showing? i ask this as i cannot find an identity that confirms this.
  2. jcsd
  3. Apr 9, 2012 #2

    Andrew Mason

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    Homework Helper

    Just use the definition of cross product of two vectors X and Y, which is a vector which has magnitude |X||Y|sinθ in a direction given by the right hand rule perpendicular to the plane of X and Y. What are the magnitudes of [itex]1/c(\vec{A})[/itex] and [itex]c\vec{B}[/itex]?

  4. Apr 9, 2012 #3
    A/c X cB by definition is the vector such that
    < A/c X cB, n > = Det [ A/c , cB, n ] for all n. By the properties of the determinant,
    Det [ A/c , cB, n ] = 1/c*c Det[A,B,n] = Det[A,B,n] = < A X B, n > for all n. Finally,
    < A/c X cB, n > - < A X B, n > = 0 for all n, so A X B = A/c X cB.

    ( < > is the inner product, or just the dot product in this case )
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