A C172 just exiting Class B airspace in cruise flight and a climbing B737 have a close encounter.

Narrative

Flying VFR at 3500 ft. MSL. I was cleared into Class B airspace; then exited the lateral boundary of the Class B to the north. Receiving radar advisories from Approach and in radio and radar contact. A B-737 was being vectored for a climb coming from the southeast; through 3500 feet (final altitude on the jet is unknown). I heard the pilot report he was responding to a TCAS resolution advisory (RA) and leveling off. ATC then advised him to stop the climb. I saw the B-737 in a moderately steep turn below my aircraft; about 500 feet below passing right to left. My aircraft is equipped with ADS-B traffic display but this position is out of the current ADS-B service area at 3500 feet. The B737; when well clear of my aircraft to the left resumed its climb with ATC clearance. Do not believe there was any threat of conflict or 'near miss'; as standard separation between an IFR and VFR is 500 feet vertically. The B737 was to my right; therefore; in visual conditions they were required to yield the right of way to my aircraft; which was to his left. Being on an IFR flight plan does not relieve the pilot from see and avoid responsibility while in visual conditions. Since ATC had both aircraft in radar contact and was vectoring both aircraft; ATC should have not cleared them to climb through 3500 feet until it was clear of my aircraft. In this author's opinion; ATC vectoring should have been performed to prevent the them from receiving a TCAS RA since both aircraft were in controlled airspace and both under radar vectors.