Show that the curve C that is parametrized by r(t) = (t² − 1, t − 2t², 4 − 6t) lies on a plane as follows:
(a) Show that the points on the curve at t = 0, 1, and 2 do not lie on a line, and find an equation of the plane that they determine.
(b) Show that for all t, the points on C satisfy the equation of the plane in (a).