Please see attachments for questions.

1. Evaluate F . dr where F(x, y, 2) = (a+y- )i+(y+ z? )j+(2+x2)k and C' is the triangle with vertices (1, 0, 0), (0, 1, 0), (0, 0, 1), oriented counterclockwise when viewed from above.2. Evaluate F . ds S where F(x, y, 2) - a yi - x y'j - a yzk and S is the surface bounded by the hyperboloid a + 12 - 22 = 1 and the planes 2 = -1, 2 = 1.3. (Extra credit). Let f and g be functions, let C' be a curve and let S be a surface. Prove the following identities. If you appeal to theorems, state which of the hypotheses of those theorems you are assuming to be true. (a) (fVg) . dr = (Vf x Vg) . ds C S (b ) ( fvf ) . dr = 0 C (c) ( (f Vg + gVf) . dr =0 C