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Math Help - vector calculus question involving del

  1. #1
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    vector calculus question involving del

    1. Problem
    What is (\vec{r} \cdot \nabla) \vec{r} ?

    where
    \vec{r} = r \hat{r} = x \hat{x} + y \hat{y} + z \hat{z}
    \nabla = \hat{x} \frac{d}{dx} + \hat{y} \frac{d}{dy} + \hat{z} \frac{d}{dz}

    2. Attempt at a Solution

    First,
    (\vec{r} \cdot \nabla) = (x \frac{d}{dx} + y \frac{d}{dy} + z \frac{d}{dz})

    Then,
    (\vec{r} \cdot \nabla) \vec{r} = x \frac{d}{dx} x \hat{x} + y \frac{d}{dy} y \hat{y} + z \frac{d}{dz} z \hat{z}

    ...since all other terms would vanish. This would reduce to,

    = x \hat{x} + y \hat{y} + z \hat{z} = \vec{r}

    Wow! Could that really be correct?
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  2. #2
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    moved from Calculus

    If someone could just look this over and let me know if I made any mistakes, that would be great. Thanks!
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