Find the unit tangent vector $T(t)$ for the function $r(t)=($:$t,t^2,t^3$:$)$ at $t=1.$

$\frac{1}{6}($:$1,2,3$:$)$

$($:$1,2,3$:$)$

$\frac{1}{\sqrt[\phantom{2}]{14}}($:$1,2,3$:$)$

$\frac{1}{\sqrt[\phantom{2}]{14}}($:$1,1,1$:$)$