$[5$pts$.]$ At which points does the curve vec$(r)(t)=$that$(i)+(2t-t^2)k$ intersect the paraboloid $z=x^2+y^2?$

$[5$pts$.]$ Sketch the curve vec$(r)(t)=t^2$hat$(i)+t^{3}j$ and indicate the orientation. Find vec$(r^{\text{'}})(t)$ and sketch vec$(r)(1)$&vec$(r^{\text{'}})(1).$