Problem 2. Prove the following identities: a) For any smooth scalar function f: R3 - R and any smooth vector field F in IR3: V . ( f F ) = VS . F+ f V . F. Conclude if F = Vg for a smooth function g, then V . (f Vg) = VS . Vg+ fAg. Use this relation and prove: Is Agav = Honda Vands - W/VS. Vedv. This is the integration by parts formula for triple integrals. In 1D, every students know the relation b) For any smooth scalar function f: R3 - R and any smooth vector field F in IR3: curl ( f F) = f curl(F) + Vfx F. Conclude that if F = Vg for a smooth function g then ofVg. dr = ( VfxVg ).nas , for any simple closed curve with positive direction, and S any surface with the boundary C