1. Denote the first 7 digits of your student number as $1828384858687. Find a vector field F: R³ → R³ that has ALL of the following four properties: (i) F is

the curl of a certain vector field, (ii) ♬ is the gradient of a certain scalar field. (iii) Each term of F is a function of x, y and z and cannot be a constant,i.e., the form of the vector field: F = f₁(x, y, z) i + f2(x, y, z)j + ƒ3(x, y, z) k. (iv) F = (s₁ + 3) + (s2₂ +2) j+($3+1) k, when (x, y, z) = ($1, 82, 83) Show the values of $1828384858687 at the beginning of the answer and your working. Explain your reasoning. Marks will be awarded for the quality of your explanation. [15 marks]