Unit Normal Vector to non-parametrized curve

**newprint** · February 25th 2009, 05:29 AM

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 ??

**Abu-Khalil** · February 25th 2009, 05:58 AM

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 $\hat{n}=\frac{\vec{n}}{||\vec{n}||}$ .

**HallsofIvy** · February 25th 2009, 07:09 AM

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= $e^t$ .

Thread: Unit Normal Vector to non-parametrized curve

LinkBack

Thread Tools

Display

Unit Normal Vector to non-parametrized curve

Similar Math Help Forum Discussions

Unit Normal Vector

Finding a unit normal vector

unit normal vector

Finding Unit Normal Vector

Unit normal vector function

Search Tags