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Vector (Cross) Product

  1. Aug 31, 2008 #1
    I was reading my physics book, and I stumbled across this : [tex]A_{x} \hat{i} \times B_{y} \hat{j} = (A_{x}B_{y})\hat{ i} \times \hat{ j}[/tex].
    I am trying to figure out, how can they use the distribute property ( I presume) like that? How did they factor the Ax and Bx out? I would have assumed it would have multiplied out like this : [tex](A_{x}B_{y})\hat{i} \times \hat{j} = (A_{x}B_{y})\hat{i\times}(A_{x}B_{y}) \hat{j}[/tex] I thought those were cross products, not multiplication signs.

    Can anyone clear up things please?

    Thanks beforehand.
    Last edited: Aug 31, 2008
  2. jcsd
  3. Aug 31, 2008 #2
    if you double A in the first equation what happens to the answer. if you double B what happens?
  4. Aug 31, 2008 #3
    BTW, cross product is not a real vector. its a pseudovector.
  5. Aug 31, 2008 #4
    I'm still lost
  6. Aug 31, 2008 #5


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    Homework Helper

    It's a property of the cross product. To show that it is permissible, ask yourself what is (AxBy) i x j? Then what is Axi X Byj ? How would you get the magnitude of the latter product? What formula should you use?
  7. Aug 31, 2008 #6


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    The standard way to take the cross product of vectors [itex]A_x\vec{i}+ A_y\vec{j}+ A_z\vec{k}[/itex] and [itex]B_x\vec{i}+B_y\vec{j}+ B_z\vec{k}[/itex] is to use the (symbolic) determinant:
    [tex]\left|\begin{array}{ccc}\vec{i} & \vec{j} & \vec{k} \\ A_x & A_y & A_z \\ B_x & B_y & B_z\end{array}\right|[/tex]

    Here, [itex]A_y= A_z= B_x= B_z= 0[/itex] so that is
    [tex]\left|\begin{array}{ccc}\vec{i} & \vec{j} & \vec{k} \\ A_x & 0 & 0 \\ 0 & B_y & 0\end{array}\right|[/tex]
    What is that?
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