1. WEN a vector field F : R3 > R3 that has ALL of the following four properties: (i) I3 is the curl of a certain vector field, (ii) F is the gradient of a certain scalar field. (iii) Each term of F" is a function ofx, y and z and cannot be a constant.i.e.. the form of the vector field: I?" = f1(a:,y,z) 7&4 f2(:c,y,z) 3+ f3(:c,y,z) E. (iv) 1?" = (31 + 3) E+ (32 + 2) 3+ (33 + 1) 1?, when cm}, 2) = (51, 32, 33) Show the values of 81328384858587 at the beginning of the answer and your working. Explain your reasoning. Marks will be awarded for the quality of your explanation