2. (a) Consider the vector field W = -xex + (x ty)ey. (i) Sketch W. In particular, identify where either the ex or ey component is zero. (ii) Show whether or not W is a conservative vector field. (b) Consider the 1-form w = A(x +y)dx + (x + y) dy where ) E R. (i) Find all values of A such that w is an exact 1-form. For each value, give the corresponding 0-form f such that w = df. (ii) Fix A = 2. Find all points P E A2 such that w (P, W(P) ) = 0. (c) Find a non-constant 0-form g such that the directional derivative Dwg is zero on all of A2