Please answer the following vector calculus problem. There are 3 parts. Let me know if you need anything else. Thank you!

4. Consider the path c : [0, 72] -> R3 given by c(t) = (6cos?(Vt), 1 - 5sin(2Vt), 8 sin?(Vt) ).(d) [8 pts] Compute the curvature of c. (e) [8 pts] Show that the curve of c lies on some plane and find the equation of the plane that contains the curve. (f) [8 pts] Find a point P = (To, yo, Zo) and a positive constant r > 0 such that I c(t) - P|| = r for all t, i.e. show that the curve of c is a circle of radius r centered at P. Hint: Part (a) and part (d) might be useful