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Problem #4: Let f : R3 > R be a smooth function. Let r(t) = (x(r),y(t),z(r)) be a smooth parametrization of a curve C in R3, [1'3 marks] where IE R, such that r00) = (l, 2, 0) for some to E i. Let f(x,y, z) = f(r(r0)) be the level surface of f such that C lies on the surface. Suppose that r'(ro) = i + j. (a) If the unit vector in the direction of Vf{r(ro)) with the positive :r-coordinate is given by At + 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 P2: + Q}: + R2 = S, where P, Q, R, S E R. Then which of the following is true? 2 l l l 1 (A)A = 33.1% 73 mm = 33.3 = 3; (CM = 33,8 || | 34 e v a II in u I ._ Pmb'em #49}: T Part (a) choices. (Ana) 1-- 43,320\") 2 jam) r (Bum 1 jun) 2 \\{5.20) r ((3)150) = 1 3:3,};{13 = 2 jam) = 0 (DMU) = 1+ grad/(f) = 2+ jam) 2 0 Problem #403}: T Part (b) choices. (A)P=1,Q= 1,.R = 0,S=1(B)P=1,Q=1,R =1,S= 0 (C)noneofthese (D)P=1,Q= 1,.R = 0,S=1 Pmb'em 'chl: T Part (5) choices