Hi

Need help on the following question:

A curve has vector equation $\displaystyle r=(3t-t^3)i+(3t^2)j+(3t++t^3)k$ Find its curvature K

i know that $\displaystyle K = \frac{|v * a|}{|v^3|}$

This is what i have done.

$\displaystyle v= (3-3t^2)i+6tj+(3++3t^2)k$

$\displaystyle a= -6ti+6j+6tk$

$\displaystyle |v * a| = \begin {bmatrix} 3-t^2 & 6t & 3+3t^2 || -6t & 6 & 6t \end{bmatrix}$

$\displaystyle i(36t^2-18+18t^2)-j(18t-18^3+18t+18t^3)+k(18-18t^2+36t^2)$

$\displaystyle i(18t^2-18)-j(36t)+k(18-18t^2)$

$\displaystyle 18t^2-18-36t+18-18t^2$

$\displaystyle |v*a|=-36t$

$\displaystyle |v| = 3-3t^2+6t+3+3t^2$

This is where i am not sure what to do

how do you work out $\displaystyle |v|^3 $???

P.S