Name: Student ID: In this quiz, we will talk about irrotational and conservative vector field. Question: Show your work. Let F(x, y, z ) = 2 + 12' 72 + 12: 0 and C be a circle on the xy-plane with parameterization r(t) = (cos(t), sin(t), 0) for t e [0, 27]. (a) Find Curl (F) = V x F. K Curl F = 1 Cy d d dx dy d2 -Y X 0 x 2 tyz x 2 ty 2 (b) Calculate fo F . dr directly. Note that by (a), F is irrotational. But based on our result in (b), F is not conservative cept the z-axis. The region is not simp