Question 5 (Unit 9) - 15 marks In Cartesian coordinates, a vector field takes the form F = 2xzi+ 2yzj+ (x' +y') k throughout the whole of three-dimensional space. (a) Find the divergence and curl of F in Cartesian coordinates. [4] (b) Use Procedure 1 of Unit 9 to express F in cylindrical coordinates (r, $, z). (c) Use your answer to part (b) to calculate the divergence and curl of F in cylindrical coordinates. Comment on the agreement with part (a). [5] Question 6 (Unit 10) - 15 marks This question concerns the vector field F defined in Question 5. (a) State whether F is conservative, and give a one-sentence justification for your statement. [2] (b) Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation r=at, y= bt, = =ct (0