7. (a) We consider the vector field F(x, y, z) = (x2, xy, 1) = 227+ xyj +12. (i) Calculate curl F DxĒ. (ii) Let the curv

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7 A We Consider The Vector Field F X Y Z X2 Xy 1 227 Xyj 12 I Calculate Curl F Dxe Ii Let The Curv 1 (75.79 KiB) Viewed 83 times

7. (a) We consider the vector field F(x, y, z) = (x2, xy, 1) = 227+ xyj +12. (i) Calculate curl F DxĒ. (ii) Let the curve C be defined by the parameterization [2 marks] C = {r(t) = (t, t’,1), te [0,1]} . Calculate 18.dr 1.di along this curve starting at the point A = (0,0,1) and ending at B = (1, 1, 1). (6 marks] (iii) Would you expect that the integral along all curves starting at point A and ending at point B would yield the same result as in part (ii)? [3 marks] (b) Use Stokes' theorem to evaluate fa- dr where G(x, y, z) = (2x, y,0) and D is any closed curve. (4 marks]