Can someone help me with calculus III

Let a and b be real, scalar constants. For the given vector field in space F(x,y,z) = (e^x+ayz)i+(e^y+xz)j+(e^z+bxy)k

What values of a and b is the vector field F(x,y,z) conservative?
Let a and b be any real-valued scalar constants, and let c be the path given by the unit circle which lies in the xy-plane oriented in the counter-clockwise direction when viewed from above (the +zaxis looking down) Calculate the line integral F of C (dot) dr

F = {e^x+ayz , e^y+xz , e^z+bxy}

according to Stokes' theorem

∮ F • dr = ∫∫ ∇ x F • ndS

for conservative potential field,

∇ x F = 0

{∂/∂x , ∂/∂y , ∂/∂z} x {e^x+ayz , e^y+xz , e^z+bxy} = {0,0,0}

{∂Fz/∂y - ∂Fy/∂z , ∂Fz/∂x - ∂Fx/∂z , ∂Fy/∂x - ∂Fx/∂y} = {0,0,0}

{e^x+ayz , e^y+xz , e^z+bxy}

bx - x = 0

b = 1

by - ay = 0

(1)y - ay = 0

a = 1


z - az = 0

z - (1)z = 0

0 = 0

OK



a = 1

b = 1