For each vector field, compute the curl and determine if there exists a function such that the vector field is equal to the gradient of that function. If no such function exists, enter NONE.

(a) Suppose vector field F(x, y, z) = (P(x, y, z), Q(x, y, z), R(x, y, z)). Compute the curl of F.

1) ∇ × F = (R_y - Q_z, P_z - R_x, Q_x - P_y)
2) ∇ × F = (Q_z - R_y, R_x - P_z, P_y - Q_x)
3) ∇ × F = (P_y - Q_x, Q_z - R_y, R_x - P_z)
4) ∇ × F = (R_y - P_y, P_z - Q_z, Q_x - R_x)