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Cross product qustion

  1. Aug 21, 2009 #1
    in the end of this
    http://i29.tinypic.com/5fktjo.jpg

    i got to the point where it asks what B is
    i think that because i X J = K then b should be in the direction of J

    but they have a different conclusion
    why??
     
  2. jcsd
  3. Aug 21, 2009 #2

    Doc Al

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    Staff: Mentor

    All you can conclude is that B has a j component.
     
  4. Aug 21, 2009 #3
    its only in j direction
    it cant have a component of other vector
    because in order to transform i to k
    we need pure j
     
  5. Aug 21, 2009 #4

    Doc Al

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    Staff: Mentor

    No. Let B = ai + bj + ck. When you take the cross product, each term must give a k-component or 0. We know that c must equal 0, since i X k = -j. But what about a?
     
  6. Aug 21, 2009 #5
    one vector is(1,0,0)
    the result vector is (0,0,1)
    i do this determinant to find the cross product
    |i j k |
    |1 0 0|
    |x y z|
    it gives us i*0 +j*z +k*-y or (0,z,-y)
    but our result vector is (0,0,1)
    so z=0 and y=-1

    y=-1 is -j vector

    there is no a here
    i showed purely by math that the result is pure -j vector

    there is no way to have components from other vectors
     
  7. Aug 21, 2009 #6

    Doc Al

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    Staff: Mentor

    No you didn't. What's i X i?
     
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