For the curve given by

$r(t)=($:$sin(t)-tcos(t),cos(t)tsin(t),3t^{2}9$:$)$

Find the unit tangent

$T(t)=($:$\frac{1}{\sqrt[\phantom{2}]{37}}sin(t),\frac{1}{\sqrt[\phantom{2}]{37}}cos(t),\frac{6}{\sqrt[\phantom{2}]{37}}$:$)$

Find the unit normal

$N(t)=($:$,$:$)$

Find the curvature

$(t)=$

$$