expressions for curvature and torsion

For a regular (http://planetmath.org/Curve), parameterized curve $\alpha :(a,b)\to {ℝ}^3$, not necessarily unit speed, the curvature $\kappa (t)$ and torsion $\tau (t)$ are given, respectively, by

$\kappa (t)$$={\displaystyle \frac{\parallel {\alpha }^{\prime }(t)\times {\alpha }^{\prime \prime }(t)\parallel }{{\parallel {\alpha }^{\prime }(t)\parallel }^3}};$

$\tau (t)$$={\displaystyle \frac{({\alpha }^{\prime }(t)\times {\alpha }^{\prime \prime }(t))\cdot {\alpha }^{\prime \prime \prime }(t)}{{\parallel {\alpha }^{\prime }(t)\times {\alpha }^{\prime \prime }(t)\parallel }^2}}.$