SCT CTLR DESCRIBED PLTDEV WHEN ACR ON DOWNWIND FOR LAX RWY 24R APPARENTLY TURNED TO HEADING 190 WHEN 090 WAS ISSUED.

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LAX OP OF VECTORING ACFT ON THE DOWNWIND FOR THE N COMPLEX. NOT SO NORMAL OP OF CLRING ACFT FOR APCH TO ILS RWY 24L WITH SIDESTEP TO RWY 24R. MODERATE OR GREATER TFC LEVEL WITH NO HDOF ASSISTING ME THE RADAR CTLR. SUPVR MONITORING FREQ INTERMITTENTLY. ACR X'S LAST INSTRUCTIONS WERE TO 'FLY HDG 090 DEGS' (TO STAY ON DOWNWIND LEG AND STAY WITHIN THE AIRSPACE FOR THE POS). ACR X READ BACK CORRECTLY BUT I NOTICED WHILE CLRING PRECEDING ACFT FOR THE APCH ACFT X WAS IN A TURN TO THE S TOWARDS IT. I INSTRUCTED ACR X TO TURN TO A HDG OF 070 DEGS AND THEY REPLIED WITH A READBACK THAT WAS PART READBACK AND PART VERIFYING. I ACKNOWLEDGE THE HDG AND ISSUED TFC TO ACFT 12 O'CLOCK POS AND 3 MI. ACFT SAID THEY WERE LOOKING. THEIR TURN SEEMED VERY SLOW. I FINALLY HAD TO ASK FOR AN IMMEDIATE TURN TO A HDG OF 060 DEGS AND TRIED TO GET SOME SORT OF SEPARATION STANDARD GOING BY ASKING THE PLTS IF THEY HAD THE TFC IN SIGHT. THEY FINALLY DID SEE THEIR TFC BUT BY THEN SEPARATION STANDARD WAS LOST (3 MI OR A THOUSAND FT). INITIALLY; I THOUGHT THAT I MAY HAVE MISSED A READBACK BY THE ACR X PLT BECAUSE OF THE PREOCCUPATION THAT CAN SOMETIMES OCCUR WITH AN UNUSUAL OP AS WELL AS A BUSY RADAR SESSION WITH NO ASSISTANCE. AFTER REVIEWING THE TAPES; IT APPEARS THE PLT READ BACK 090 DEG HDG AND SOMEHOW TURNED TO A 190 DEG HDG (OR A HDG CLOSE TO). IT SHOULD BE NOTED THAT THE DOWNWIND WAS EXTENDED AT THE TIME DUE TO SECTOR SATURATION AND; COINCIDENTALLY; ACFT HAD TURNED AT THE 'TARGET POINT' THAT WE STRIVE FOR. AT THE TIME THERE WAS A SLIGHT WIND FROM THE N AND I THINK THAT SLOWED UP THE ACFT'S TURN RATE BACK TO THE DOWNWIND. FINALLY; I CAN ONLY SPECULATE BUT IT SEEMED HIS TURN TO THE DOWNWIND WAS SLOWER (EVEN WITH A TAILWIND) BECAUSE IT WAS DOING WHAT ALL LNDG AIRPLANES HATE TO DO (TURN AWAY FROM THE ARPT). SUPPLEMENTAL INFO FROM ACN 795601: AT 2500 FT ON EXTENDED DOWNWIND INTO LAX RWY 24L ON A HDG OF 065 DEGS; WE WERE GIVEN A TURN TO 180 DEGS. WHILE IN THE TURN TO 180 DEGS; ATC CALLED TFC AT 12 O'CLOCK POS AND GAVE US A TURN BACK TO 070 DEGS. ON TAXI IN; WE WERE GIVEN A PHONE NUMBER TO CALL REGARDING A POSSIBLE LOSS OF SEPARATION. I CALLED THE FACILITY AND WAS TOLD THAT WE TURNED TO THE WRONG ASSIGNED HDG. BOTH THE PF AND I WERE CERTAIN THAT WE FOLLOWED ATC INSTRUCTIONS AS GIVEN.