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2. Consider the cylindrical vector eld Q(p,, z) = 1 329 + 1 Egg, + 1 322. The left panel below shows a view of Q slightly offset from the positive z-axis; the rotating nature of the vector eld is evident. The right panel shows a different view of the vector field, illustrating the cylindrical paths in (i), (ii), and (iii). Compute the following line integrals using it; E nip p + ,0 dc!) 31, + dz z. . f 1 W 4": i- ' I' 1 (i) W]: G . 513: where ti: = arr/4, z = 1, and ,9 changes from 1 t03 on C1. C1 (ii) W2 =/ G - dr wherep = 31 z = 1, and (15 changes from 713/4 to 17/2 on CQ. (:2 (iii) W3 =f Q - g; wherep = 31 $5 = f2, and 2 changes from -1 to 2 on C3. C3