FLC RECEIVES TCASII RA AFTER RECEIVING MCO APCH CLRNC TO SFB RWY 9L.

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DURING INITIAL RADAR VECTORS FOR ARR TO SANFORD; FL; ORLANDO APCH ADVISES ACFT X TO TURN R; HDG 270 DEGS; MAINTAIN 3000 FT; RADAR VECTORS FOR ILS RWY 9L. ACFT X ACKNOWLEDGED. ATC CLRED ACFT X TO TURN L; HDG 80 DEGS FOR VISUAL APCH RWY 9L. ACFT X ADVISED HE IS REQUESTING RADAR VECTORS ON TO THE LOC FOR THE ILS; NINE L. ATC TURNED ACFT X R HDG 230 DEGS FOR THE ILS APCH RWY 9L. ATC THEN CLRED ACFT X TO TURN L 180 DEGS MAINTAIN 2000 FT. ACFT X ACKNOWLEDGED (DELAYED ON THIS HDG UNTIL WE PASSED THROUGH THE LOC; I WAS THINKING AT THE TIME; THIS WAS PROBABLY BECAUSE TFC PREVENTING A TURN TO INTERCEPT THE LOC). ATC CLRED ACFT X TO 'TURN L; HDG 070 DEGS TO INTERCEPT THE LOC; MAINTAIN 2000 FT UPON INTERCEPT; AND YOU ARE CLRED FOR THE ILS APCH RWY 9L. DURING MY READBACK; WE RECEIVED AN RA. WE INITIATED A CLB; AND ALMOST IMMEDIATELY AFTER; APCH CTL DIRECTED US TO CLB TO 2100 FT. THE FE STOOD UP FROM HIS SEAT AND STATED THAT A SMALL ACFT; WHICH LOOKED LIKE A CESSNA; WAS PASSING DIRECTLY BELOW US. THE SEPARATION INDICATION ON THE TA-RA READ 300 FT.