Falcon 900
ATC Issue All Types; Conflict Airborne Conflict
Flight Crew Took Evasive Action
Procedure
The event occurred while being vectored onto VOR RWY 6 approach into APC. We were at 4;000 feet and were told to turn left to join approach course. The TCAS system then gave us a Resolution Advisory to DESCEND immediately after reading back our instructions. The autopilot was disengaged and we descended following our VSI. The TCAS system then gave us another Resolution Advisory to CLIMB while we were in the descent. The Resolution Advisory was followed exactly how we are trained. CLEAR OF CONFLICT was announced and we saw the small Cessna pass below us off our left wing. If we would have taken the turn we would have been pointed directly at the traffic that caused our Resolution Advisory.There needs to be better separation between VFR and IFR traffic in this area.
[Report narrative contained no additional information.]
Falcon 900EX flight crew reported receiving an RA on approach to APC when ATC gave them a turn clearance; which they felt could have resulted in a collision had it been followed.