Consider the trajectories vec$($r$)($t$)=$that$()+$t$^(2)$hat$($j$)$ and vec$($s$)($t$)=3$that$()-$that$()+2$tk$.$

$2$ a$.$ Find the unit tangent to vec$($r$)$ at t$=0.$

b$.$ Find the equation of the line tangent to vec$($r$)$ at t$=0.$

c$.$ Compute the normal component of vec$($s$).$

d$.$ Consider the $\backslash$lim$\_($t$->\backslash$infty $)$a$\_($N$)$ for the normal component computed in part c$.$ Interpret the

results of that calculation.

$(5$ points each$)$