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Problem #4: Let f : [R3 > R be a smooth function. Let r(t) = (370'), y(t), 20)} be a smooth parametrization of a curve C in R3, [10 marks] where IE R, such that r00) = (1, 2, 0') for some to E R. Let f(x,y, z) = f(r(t0)) be the level surface of f such that C lies on the surface. Suppose that r'(to) = i + j. (a) If the unit vector in the direction of V f (11319) with the positive sac-coordinate is given by Ai + B j. Then which of the following is true for A and B? (b) Find the parametric equation of the normal line at r60). (c) If the tangent plane of the level surface at the point r00) is given by Px + Qy + R2 = S, where P, Q, R, S E R. Then which of the following is true? 2 1 l 1 1 (A)A = 3'32 33 (B)A = 33,3 = 33 (C)A = 33.3 II I H 3 ha. II in II I _ \"Oman" #4\"): T Part (a) choices. t t (Amt) 1 43,110 2 Two) r (Ema 1+ jam) 2 $.20) r (C)x(t) = 1+ 3341:) = 2 jam) = 0 (mm) = 1+ 53%;) = 2+ 33,2\") = 0 \"Omar\" #409}: T Part (D) choices. (A)P=1,Q= 1,R = 0,S=1 (B)noneofthese (C)P=1,Q = 1,R= 0,S=l (D)P=1,Q=1,R=1,S=0 Pmb'em #493}: T Part (:3) choices