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Clear up some cross product confusion for me

  1. Feb 19, 2012 #1
    Here is what I have

    A=xro+yr1

    B=yro+xr1


    I need to find A x B

    I am confused about do it because The components of A and B are in terms of vectors

    If A = 3i + 4j + 7k and B = 2i + 2j + 1k I would have no problem (these numbers are meaningless just giving an example) finding A x B but I don't have components I have vectors. Can some one explain how to do this. Thanks
     
  2. jcsd
  3. Feb 19, 2012 #2
    Could I set it up as follows

    Sorry I don't no how to input a matrix hopefully this can get the idea across
    ro r1 k ro r1
    x y 0 x y
    y x 0 y x

    and then do the normal cross product thing where you multiply diagonals and so on. The thing that troubles me is there is really no k component. The only thing I know is my answer will be perpindicular to the plane with r0 and r1 so not sure what to do
     
  4. Feb 20, 2012 #3

    mathman

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    AXB = (x2 - y2)r0Xr1.

    I am assuming x and y are scalars.
     
  5. Feb 20, 2012 #4

    tiny-tim

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    hi 2slowtogofast! :smile:
    hints: distributive law

    what are ro x ro and r1 x r1 ? :wink:
     
  6. Feb 20, 2012 #5
    @tinytim

    roxro = 0 I can see how that will simplify things I am confused about the distributive law part

    A x (B+D) = (AxB)+(AxD)

    I have somthing more like this

    (xro+yr1) x (yro+xr1) = (xro+yr1) x yro + (xro+yr1) x xr1

    Use the distributive rule again on the RHS

    (xro x yro) + (yr1 x yro) + (xro x xr1) + (yr1 x r1)

    Then the first and last terms are 0. Am on the right track or did I make a wrong turn somewhere
     
  7. Feb 21, 2012 #6

    tiny-tim

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    hi 2slowtogofast! :smile:

    (just got up :zzz:)
    yes :smile:

    now what is the relationship between r1 x ro and ro x r1 ? :wink:
     
  8. Feb 21, 2012 #7
    r0 x r1 = -(r1 x r0)

    If that is correct i think i can take it from there thanks for the help
     
  9. Feb 22, 2012 #8

    tiny-tim

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    that's it! :smile:
     
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