1. Consider the vector field: F(x, y,z) = ((y+z)et,et,e*). (a) (1pt) Find curl(F) . (b) (1pt) Find div (F) . (c) (1pt) Use your answer to (a) or (b) and previously discussed theorems to determine whether or not F(x, y,z) is a conservative vector field. Briefly explain your reasoning. (d) (1.5pts) Suppose C is any path from (0,0,0) to (a, ,d2,d, ). Show that | F. dr = div(F)(a,, az , a; ). Note: div(F) (a, ,a, ,a, ) means the divergence of F (i.e. what you found in (b)) evaluated at (a, , az , a; )