Find the curvatureKof the curve.

$\displaystyle r(t) = < e^t cos(t) , e^t sin(t) , e^t >$

I have:

$\displaystyle

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

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

$

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

e^t cos(t) + e^t sin(t) + e^t cos(t) - e^t sin(t), e^t >

$

Combine like terms:

$\displaystyle

r''(t) = <- 2e^t sin(t) , 2e^t cos(t) , e^t >

$

I have that curvature is

$\displaystyle

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

$

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

$\displaystyle

<e^{2t} [sin(t)-cos(t)], -e^{2t} [sin(t)+cos(t)], 2e^{2t}>

$

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