Consider the following vector function.

$r(t)=($:$3t,\frac{1}{2}{t}^2,t^2$:$)$

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

$T(t)=$

$$

$$

$N(t)=$ Your answer cannot be understood or graded. More Information

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

$x(t)=$ Your answer cannot be understood or graded. More Information