LOSS OF TFC SEPARATION BTWN AN ARR EMB145 AND A STUDENT PLT IN A KATANA MAKING A NORAC APCH TO THE WRONG RWY AT BWI; MD.

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WE WERE BEING VECTORED ON A WIDE R DOWNWIND TO RWY 33L AT BWI WITH POTOMAC APCH. TFC WAS CALLED AND SPOTTED BY MY FO; A SINGLE ENG ACFT THAT WAS VECTORED FROM L TO R 1000 FT BELOW US. AFTER THE ACFT PASSED BY; WE CALLED THE FIELD AND WE WERE CLRED FOR THE VISUAL TO RWY 33L. DURING OUR TURN TO FINAL WE LOST VISUAL CONTACT WITH THE ACFT AND INFORMED APCH CTL THAT WE NO LONGER HAD THE ACFT IN SIGHT. THE CTLR STATED THAT IT WAS NO FACTOR AND STATED AGAIN THAT WE WERE CLRED FOR THE VISUAL RWY 33L AND GAVE US A FREQ CHANGE TO BWI TWR. AS WE WERE SWITCHING TO THE TWR FREQ I SPOTTED A TARGET ON OUR TCASII COMING TOWARDS OUR FLT PATH. THE ACFT WAS CONVERGING WITH OUR FINAL AND I REMEMBER OUR TCASII SHOWING IT 200-400 FT BELOW US. WE CHKED IN WITH TWR AND INQUIRED AS TO THE OTHER ACFT'S POS AND INTENTIONS. THE TWR CTLR STATED THAT SHE HAD BEEN UNABLE TO RAISE THE OTHER ACFT. WE RECEIVED A TA FOLLOWED BY AN RA WITH 'MONITOR VERT SPD' AND THEN A 'CLB' ADVISORY. I BROUGHT FULL PWR UP ON OUR ACFT AND INITIATED A CLBING L TURN IN RESPONSE TO THE RA. MY FO SAID THAT WHEN HE SPOTTED THE ACFT AGAIN IT WAS APPROX 1/2 TO 1/4 MI AND CLOSING AND APPROX 200 FT BELOW OUR ALT. I SPOKE WITH BWI TWR AND POTOMAC APCH ONCE ON THE GND. I WAS TOLD THAT THE ACFT IN QUESTION WAS A STUDENT PLT ON SOLO FLT THAT HAD BEEN NAVING FOR RWY 33R. I HAVE SPOKEN WITH A NUMBER OF SUPVRS AT POTOMAC TRACON AND HAVE BEEN ASSURED THAT THEY WILL CONTACT ME WHEN THE TAPES HAVE BEEN REVIEWED. I HAVE YET TO HEAR FROM THEM. I THINK SOMEONE SHOULD TALK TO THE FLT INSTRUCTOR/CHIEF FLT INSTRUCTOR OF THE FLT SCHOOL IN QUESTION.