# Thread: Finding curvature

1. ## Finding curvature

Find the curvature K of the curve.
$r(t) = < e^t cos(t) , e^t sin(t) , e^t >$

I have:
$
r(t) = < e^t cos(t) , e^t sin(t) , e^t >$

$r'(t) = < e^t cos(t) - e^t sin(t), e^t sin(t) + e^t cost(t), e^t >
$

$r''(t) = < - e^t cos(t) - e^t sin(t) + e^t cos(t) - e^t sin(t) ,$ $
e^t cos(t) + e^t sin(t) + e^t cos(t) - e^t sin(t), e^t >
$

Combine like terms:
$
r''(t) = <- 2e^t sin(t) , 2e^t cos(t) , e^t >
$

I have that curvature is

$
\kappa = \frac{|r' \times r''|}{|r'|^3}
$

For the numerator I crossed r' and r'' and got:

$

$

I don't know how to convert this into a magnitude; same for denominator.

2. The magnitude of a vector $|\vec{v}|=\sqrt{\vec{v}\cdot\vec{v}}$.

3. I got down to $\frac{root{2}}{3e^t}$

That look right? :/

4. Can you clean up the LaTeX code a bit?

5. Tried to make it more legible.

6. Try this: $\frac{\sqrt{2}}{3e^{t}}$. You can click on the equation I just wrote down to see what LaTeX code I wrote to obtain it.

That's what I got as well. Looks good!