1. For each of the following, sketch the trace of (¢, R), describe its orientation, and verify that it is a subset of the surface S.

(a) ¢(t) = (3t, 3 sin t, cos t), S = {(x, y, z) : y2 + 9z2 = 9}.

(b) ¢(t) = (t2,t3,t2), S= {(x,y,z): z=x}.

(c) ¢( t) = (t, t2 , sin t), S = {(x, y, z) : y = x2 }.

(d) ¢(t) = (cost,sint, cost), S= {(x,y,z) :y2+z2 = I}.

(e) ¢(t) = (sint,sint,t), S = {(x,y,z): y = x}.