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Thread: 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 $\displaystyle \mathbb{R}^2$ or $\displaystyle \mathbb{R}^3$?

    Anyway, if you derivate you'll get $\displaystyle \frac{dy}{dx}=e^x$, so the tangent line in $\displaystyle x=1$ has a slope equal to $\displaystyle e$, therefore the normal line to the curve in that point has a slope $\displaystyle -\frac{1}{e}$. Let $\displaystyle \vec{n}=\left(1,-\frac{1}{e}\right)$ then your vector is $\displaystyle \hat{n}=\frac{\vec{n}}{||\vec{n}||}$.
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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= $\displaystyle e^t$.
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