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Math Help - Cross/Dot Product

  1. #1
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    Cross/Dot Product

    Hey, I'm stuck on one problem for my homework (LAST ONE!!) It seems really simple but I can't figure it out. Here it is:

    Express the vector A = 2i - 3j + 5k as a sum A = B + C, where B is parallel to the vector V = 3i -2j +5k and C is perpendicular to V.

    Here's what I know:
    B x V = 0, because B is parallel to V
    C (dot) V = 0, because C is perpendicular to V

    However I can't find a way to apply the above

    Thanks!
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  2. #2
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    B=[(A.V)/(V.V)]V and C=A-B, where (A.V) is the dot product of A and V.
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  3. #3
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    Hello, Raman!

    There are formulas for this problem . . .


    Express the vector: .A .= .2i - 3j + 5k .as a sum .A .= .B + C,
    where B is parallel to the vector V .= .3i - 2j + 5k, and C is perpendicular to V.
    Code:
                              *
                     A    *   :
                      *       : C
                  *           :
              *---------------+-------*
              : - - - B - - - :
              : - - - - - V - - - - - :

    Given vectors A and V . . . B is the projection of A onto V.

    . . . . . . . . . . . . . . . . .AV
    The formula is: .B . = . ----- V
    . . . . . . . . . . . . . . . . .|V|

    . . . . . . . . . . . . . . .[2,-3,5][3,-2,5] . . . . . . .37
    So we have: .B . = . --------------------- V . = . --- V
    . . . . . . . . . . . . . . .(√3 + 2 + 5) . . . . . .38

    Hence: .B .= .(37/38)[3,-2,5] .= .[111/38, -74/38, 185/38]



    Another formula: . C .= .A - B

    Hence: .C .= .[2, -3, 5] - [111/38, -74/38, 185/38] .= .[-35/38, -40/38, 5/38]



    Therefore: .A .= .[111/38, -74/38, 185/38] + [-35/38, -40/38, 5/38]

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  4. #4
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    Thanks!

    Wow, thanks a LOT, that picture/diagram really makes it all clear! Great explaination btw as well. Once again, thank you, both of you!
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