Exercise 4. Demonstrate that the vector field u(x, y, z) = yzi+zxj + xyk is both irrotational ( x = 0) and solenoidal (u= 0). Find a scalar function (x, y, z) such that u = - (we call the scalar potential for u(x, y, z)). Can you find a vector field Ä such that the curl of A is ? If u were to be a magnetic field, what does this state about regions where this is true?