Military crew reported a near miss and TCAS RA with another aircraft while under ATC control. The pilot maneuvered the aircraft; following the TCAS RA guidance then landed safely.

Narrative

While under positive control receiving radar vectors to ZZZ 1:35 minutes into our flight at 3;000 ft MSL with a heading of 011 going 190 MPH. We overheard ATC talking to another aircraft in our vicinity; the other aircraft was directed to maintain 3;500 ft MSL and maintain current heading. On TCAS; we monitored an aircraft with a path directly opposite of our path (Heading directly toward our nose) enter into our 5 NM ring. ATC did not mention the aircraft nor let the other aircraft know we were on a path just off their nose. The TCAS system gave us a resolution advisory with direction to descend immediately. The Pilot on the controls disengaged the autopilot system and dove approximately 300 feet to react to the advisory. We immediately notified ATC that we were responding to an RA and were now going back to our assigned heading and altitude. ATC acknowledged the RA situation and told us to report when completed with the RA. The rest of the flight was un-eventful; and we safely landed at our destination. Immediately after landing the pilot and Co-pilot debriefed the situation and came to the conclusion that ATC never alerted either aircraft to the converging traffic.