Question: 2. (10 marks) Consider the vector field F = (y?, x, 23) and let C be the in- tersection curve of the paraboloid z =

2. (10 marks) Consider the vector field F = (y?, x,

2. (10 marks) Consider the vector field F = (y?, x, 23) and let C be the in- tersection curve of the paraboloid z = 5 - (x2 + y?) and the plane z = 1 oriented counterclockwise when viewed from high above the plane. (a) Parameterize the curve C . [1] (b) Use the parametrization in Part a) to evaluate the line integral. (3] OF . dr. Jc (c) Let S be the part of the paraboloid z = 5 - (x2 + y?) above the plane z = 1 oriented upward, in the positive direction of z-axis. Parame- terize S and use the parametrization to evaluate the surface integral (curl(F) . n) ds. S [5] (d) You are supposed to get the same answers for Part b) and Part c). Explain why. [1]

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