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Math Help - Unit Normal Vector to non-parametrized curve

  1. #1
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    Unit Normal Vector to non-parametrized curve

    I got a curve, that is non parametrized and I need to find principal unit normal vector to that curve at certain point

    in my case it is y=e^x at point x=1

    what do I do ??
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  2. #2
    Member Abu-Khalil's Avatar
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    In \mathbb{R}^2 or \mathbb{R}^3?

    Anyway, if you derivate you'll get \frac{dy}{dx}=e^x, so the tangent line in x=1 has a slope equal to e, therefore the normal line to the curve in that point has a slope -\frac{1}{e}. Let \vec{n}=\left(1,-\frac{1}{e}\right) then your vector is \hat{n}=\frac{\vec{n}}{||\vec{n}||}.
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  3. #3
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    It's actually unusual for a curve in two dimensions as parametric equations since it is simpler to write it as a single xy equation. If that was a problem and you knew how to find a normal vector for a parameterized curve, let x itself be the parameter: x= t, y= e^t.
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