see if you are comfortable with the wedge product and exterior derivative of differential forms in R\". (a) Consider the 1-forms wi = yda + rdy + zdz and w2 = adx + zdy + ydz in RS. Compute their wedge product, w1 A w2. Note that wj A w2 is a 2-form on R", so you want to put it in the form W1 Aw2 = A(x, y, 2) dy / dz + B(x, y, z) dz A dx + C(x, y, 2) dx A dy. (b) Now recall that 1-forms on R" are represented by vector fields. For example, wj is represented by the vector field F = (y, x, z), and w2 is represented by the vector field G = (x, z, y). Compute the cross product F x G. (c) Finally, recall that 2-forms on R" are also represented by vector fields: we say that the 2-form Ady Adz + Bdz Adx + C dx / dy is represented by the vector field (A, B, C'). Now compare your answers in (a) and (b), and fill in the blanks (with the name of the suitable operation): . upon identifying 1-forms and 2-forms on R with vector fields, we see that the product of 1-forms is represented by the product of vector fields. (Note that for this identification to be correct, we really need to write the 2-form in that specific form with dy A dz, dz A de and da A dy!)