Consider a coordinate system defined by

x = u^2 v^2

y = 2uv

z = w

(a) Calculate the unit vectors _u, and _v. Clearly _w =k. Show that the unit vectors are mutually orthogonal.

(b) Calculate the scale factors h_u and h_v. Clearly h_w = 1.

(c) Calculate the divergence and curl of the field F = v^2_u + u_v + 2_z