Which of the (i) F(x, y) = (10xy+6) i + (9xy+8) j (ii) F(x, y) = (9ye⁹x + cos 6y)i + (x + 6x sin 6y) j e10xy j (iii) F(x, y) = 10y²e1¹0xyi + (10+xy) e¹ following vector fields are conservative?

1. (Section 17.1) Match the vector fields with their sketches below by placing the letter of the function in the corresponding blank: (I) F(x, y) = (II) F(x, y) = (III) F(x, y) = (IV) F(x, y) = Vector Field: (B) Vector Field: (A) (C) Vector Field (D) 0 Vector Field:

3. (12) Let V = R². Define vector addition and scalar multiplication as follows: (u1, uz)O(v1, v2) = (u1V1, U2V2) and c(u1,u2) = (u,C, u2^), c > 0 (a) Does V have an additive identity? If so, what would it be? (b) Does the distributive axiom c(uOv) = cu@cv hold? (Show why or why not). 4