The u-, v-, z-coordinate system frequently used in electrostatics and in hydrodynamics is defined by xy...

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The u-, v-, z-coordinate system frequently used in electrostatics and in hydrodynamics is defined by xy = u, x - 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 v 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, x ê, = +ê,) or left-handed (ê, x êy =-ê)? %3! The u-, v-, z-coordinate system frequently used in electrostatics and in hydrodynamics is defined by xy = u, x - 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 v 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, x ê, = +ê,) or left-handed (ê, x êy =-ê)? %3!