The u-, v-, z-coordinate system frequently used in electrostatics and in hydrodynamics is defined by xy=u, x²-y²=v, z=z. This u-, v-, z-system is orthogonal. (a) In words, describe briefly the nature of each of the three families of coordinate surfaces. (b) Sketch the system in the xy-plane showing the intersections of surfaces of constant u and surfaces of constant u with the xy-plane. (c) Indicate the directions of the unit vectors ê, and ê, in all four quadrants. (d) Finally, is this u-, v-, z-system right-handed (ê, xê₁ = +êz) or left-handed (ê, x ê₁ = -ê₂)?