see if you are comfortable with integrating 1-forms in R.".For the next problems, let M be the intersection of the surfaces x - y' = 1 and z = y". Let P = (To, yo, 20 ) be a point on M, and let C be the portion of M between the points (1, 0, 0) and P. (a) To warm up, sketch the surfaces x - y" = 1 and z = y, and sketch the curve M of intersection. (b) Find a parametrization for C, clearly indicating its domain. What are the starting and ending points associated with your parametrization? Hint: let y = t. (c) Now, consider the force field given by F(x, y, z) = (y, x - 1, z - 3). Recall that the work 2 done by F to move a particle along an oriented curve is the line integral of F along this curve. Let W denote the work done by F to move a particle along our curve C going from (1, 0, 0) to P. Show that W = yo. (c) Suppose M models a piece of wire with mass density given by H(x, y, 2) = Vx+ 3y2 +42. measured in g/ m. Find the mass of the portion of this piece of wire between the points (1, 0, 0) and (2, -1, 1)