Determine whether the given vector field is conservative. If so$,$ evaluate the line integral using the condition vec$(F)=$gradf.

a$.$ vec$(F)=[e^{2z},3y^2,\frac{1}{z}]$ from $(1,2,1)$ to $(3,4,1)$

b$.$ vec$(F)=[e^{x}siny,e^{x}cosy]$ from $(0,0)$ to $(0,2)$