L1011 ON VECTOR HDG FROM APCH CTLR HAD TCASII RA ON ANOTHER ACFT AND RPTR ACFT CLBED TO AVOID TFC.

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UP TO THIS TIME EVERYTHING WAS NORMAL AND WE HAD SWITCHED TO THE SECOND SOCAL APCH CTLR FOR FINAL VECTORS TO RWY 24R AT LAX. HE CLRED US TO DSND FROM 7000 FT TO 2500 FT. DURING THE DSCNT WE WERE VECTORED ON A 030 DEG HDG FOR A FEW MINS; THEN BACK TO 070 DEGS. PASSING 3000 FT I NOTICED TFC AT OUR 10 O'CLOCK POS WITH AN ASSOCIATED 'TFC; TFC' TA. THEREAFTER; THE CTLR DISTR MY ATTN WITH A HDG CHANGE TO 160 DEGS FOR BASE LEG. IMMEDIATELY WE GOT AN RA AND A 500 FPM GREEN VSI COMMAND WITH VERBAL 'CLB.' THE FO WAS FLYING. HE IMMEDIATELY CLBED TO 3000 FT WHILE TURNING R. I INFORMED THE CTLR BUT 2 CALLS WERE REQUIRED BEFORE HE FINALLY ACKNOWLEDGED WITH 'ROGER.' AFTER WE WERE CLR THE FO DSNDED BACK TO 2500 FT. ALL THIS HAD HAPPENED INSIDE A CLOUD LAYER SO WE NEVER MADE VISUAL CONTACT WITH THE TFC. THE REMAINDER OF THE FLT WAS VFR AND UNEVENTFUL. I BELIEVE THE PROB AROSE WHENEVER WE WERE VECTORED AWAY FROM OUR 070 DEG HDG TOWARD THE N (030 DEGS) FOR SEQUENCING; BUT THAT IS ONLY A SUPPOSITION ON MY PART. IN THE LEAST; I WAS REMINDED ABOUT JUST HOW CONGESTED THE LOS ANGELES BASIN CAN BECOME DURING PERIODS OF FREQUENT ARRS. TCASII HAS ALREADY PAID FOR ITSELF TIME AND AGAIN SINCE ITS INSTALLATION WITH THE AIRLINES AND I WAS GRATEFUL WE WERE ABLE TO BENEFIT DURING THIS FLT.