Find both lines which intersect the $z-$axis and are tangent to the curve $r(t)=($:$t^2-3t,t+1,t^3+5t$:$).$ You can give the answer$($s$)$ in either vector form or parametric form; simplify your answers. $($Hint: points on the $z-$axis are of the form $(0,0,z).)$