2. A vector field is defined in a Cartesian coordinate system by 22 3 vec(A) = 3xy zhat(1) + 2xyzhat(1) + xyhat(k) (a) Show that for this field vec(grad) x vec(A) = vec(0). (b) The previous result implies that vec(A) = vec(grad), where p is a scalar function of position. Determine (x, y, z) subject to the condition that p = 0 at the origin. (c) The curve C is defined parametrically by x = t, y = 2t,z= t from t = 0 to t = 1. i. Show that, along C, 4 = 4t. ii. Evaluate fdvec(r) where vec(r) is the position vector of a point on C.