Question Number 5115 by Yozzii last updated on 14/Apr/16
$${Given}\:{the}\:{space}\:{curve}\:\boldsymbol{{r}}=\boldsymbol{{r}}\left({t}\right),\:{show} \\ $$$${that}\:{its}\:{torsion}\:\tau\:{is}\:{given}\:{by} \\ $$$$\tau=\frac{\overset{.} {\boldsymbol{{r}}}\bullet\overset{..} {\boldsymbol{{r}}}×\overset{...} {\boldsymbol{{r}}}}{\mid\overset{.} {\boldsymbol{{r}}}×\overset{..} {\boldsymbol{{r}}}\mid^{\mathrm{2}} }.\:{It}\:{may}\:{help}\:{to}\:{know}\:{that}\:{its} \\ $$$${curvature}\:{is}\:{numerically}\:{given}\:{by}\:\kappa=\frac{\mid\overset{.} {\boldsymbol{{r}}}×\overset{..} {\boldsymbol{{r}}}\mid}{\mid\overset{.} {\boldsymbol{{r}}}\mid^{\mathrm{3}} }. \\ $$$$\overset{.} {\boldsymbol{{r}}}\:{is}\:{differentiation}\:{of}\:\boldsymbol{{r}}\:{once}\:{with} \\ $$$${respect}\:{to}\:{t}. \\ $$