Consider the following vector function.

$r(t)=($:$t,t^2,4$:$)$

$($a$)$ Find the unit tangent and unit normal vectors $T(t)$ and $N(t).$

$T(t)=$

$N(t)=$

$$

$($b$)$ Use the formula $x(t)=\frac{|T^{\text{'}}(t)|}{|r^{\text{'}}(t)|}$ to find the curvature.

$x(t)=\frac{|8t^2-2|}{(14t^2)}$