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Vectors: cross product question

  1. Feb 17, 2008 #1


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    If a, b, and c are vectors, and a=b x c, and a and c are known, how do I solve for b?

    b=a/c ? I don't think we've covered diving vectors, and since the cross-product is a special case of multiplying vectors (as opposed to dot product), I'm not sure this is allowed anyway.

    I'm trying to compute dipole moment, given a torque and an electric field. In my above example, a is torque, and c is electric field. I need to solve for b.

  2. jcsd
  3. Feb 17, 2008 #2
    We know that a is orthogonal to vector b & c, hence the cross product. So, one way to know if two vectors are orthogonal is proving that the dot product is 0.

    Let [tex]b=<b_1,b_2,b_3>[/tex]

    [tex]b\cdot(b \ x \ c)=0[/tex]

    There should be a property and perhaps an example on how to do this operation. If you are unable to find it, let me know and I will show you.
    Last edited: Feb 17, 2008
  4. Feb 17, 2008 #3


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    Thanks for your reply.

    There are similar examples in our notes where we find the torque, but not the dipole moment. At first glance, this looked like an easy problem. I'm a little confused by the direction you're going, since "a" has not been used.

    I'm going to change the variables from a b & c to t (torque), p (dipole moment), and E (electric field) just to be consistent. (t is actually tau, but you get the point).
    E= 3.7*103 , 30°
    solve for p

    And from class notes,
    t= p x E
  5. Feb 17, 2008 #4
    What are the points for vectors a & c? And I am using a, it's (b x c).
  6. Feb 17, 2008 #5


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    sorry, I switched the variable names. a became t. b became p, and c became E.
    So we bave t = p x E. Solve for p, with t and E given.
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