Let F(x, y, z) = ryi + yzj+ zæk and C be the boundary of the part of the paraboloid z = 1- x² – y? in the first octant. The curve C is oriented anticlockwise when viewed from above. (a) Which of the...

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Extracted text: Let F(x, y, z) = ryi + yzj+ zæk and C be the boundary of the part of the paraboloid z = 1- x² – y? in the first octant. The curve C is oriented anticlockwise when viewed from above. (a) Which of the following theorems most helpful in evaluating ſe F - dr? (1) The Fundamental Theorem of Line Integral (2) Green's Theorem (3) Stokes' Theorem (4) Divergence Theorem (b) Let S:r(u, v) = ui + vj + (1 – u² – v²)k with u² + v² < 1,="" u=""> 0, v > 0 Consider a normal vector (a, b, 1) of S at (,, }). What is the value a+b? (c) Let vii+vzj+v3k be the curl of F at point (,,5). What is vi +v2 –2v3? 23 of 24 (d) Evaluate 20 S. F · dr. Your answer to (a), Your answer to (b) , Your answer to (c), Your answer to (d) .