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Math Help - Vector Calculus

  1. #1
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    Vector Calculus

    A quick question. I'm trying to deduce what the following basis are:
    -z\hat{j} + y\hat{k}

    And

     x\hat{k} - z\hat{i}

    I know for instance

    x\hat{i} + y\hat{j} = {\hat{a}}_{r}r
    -y\hat{i} + x\hat{j} = {\hat{a}}_{\phi}r

    But how would i deduce the first two?

    Thanks
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  2. #2
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    Re: Vector Calculus

    These symbols mean nothing if you don't give them a meaning by defining them.
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  3. #3
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    Re: Vector Calculus

    Well i, j and k are the basis that translate to x, y, z.

    a_r and a_phi are the basis for polar coordinates i believe.
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  4. #4
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    Re: Vector Calculus

    Then your problem makes no sense. Your \hat{i}, \hat{j}, and \hat{k} are three dimensional while \hat{a_r} and \hat{a_\phi} are two dimensional. You will have to complete that by using cylindrical coordinates ir spherical coordinates.
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