Consider the vector eld Fl(m, y, z) = {4 I}; + (Q '92 322)}+(18yz)l (a) Show that V x F = fl. (is) If there exists a scalar function @(93, y, 2) such that F = Vii, find Ii using a systematic method. If not, explain how you know no such *f- exists. Now consider the cone with circular cross section whose vertex is at a: = 0. y = 0. z = 6 and whose base is the enclosed area of the circle of radius 6 in the myplane centred at the origin. Let 31 be the (curved) side wall, and 3'2 be the (at) base. Let C be the circle where the two surfaces intersect. parametrized by z = 6 cos(t). y = Gain). (c) Sketch the cone. labelling S], 32, and C. Show the direction of the parametrization of C. (d) Using any tools you have learned in this subject. calculate f0 1?\" - all: We have learned several ways to do this integral. It mayr help to use the result given in (a) and Stokes Theorem. or use {b} and a result about potentials. (.9) Find a: V-F'. (f) Find LUV V - GdV where V is the interior of the cone. which you can assume has volume 631r/3. Explain your work. r [9) Using (f) and the Divergence Theorem; nd 1.51 13" - (79 + H3: I7 - d3