LESS THAN STANDARD SEPARATION BETWEEN ACR-SMT AND UNK BOTH ON VECTORS FOR PARALLEL APCHS.

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I WAS CAPT OF AN SMT FLT SCHEDULED FOR XA10 AM; ARR INTO LAX IN 8/88. WE WERE ARRIVING FROM SBA; AND IN SEQUENCING US FOR APCH AND LNDG; LAX APCH ISSUED A CLRNC OF 160 DEGS ON THE HDG AND DSCNT TO 2500' UNTIL CONTACTING TWR; EXPECTING LNDG ON RWY 24R. I COMPLIED WITH THE CLRNC; MY F/O WAS XMITTING ON THE #2 RADIO AND BRIEFING PAX. I NOTICED SOME INTERFERENCE WITH THE AUDIO ON #1 AS A RESULT. HOWEVER; I DID NOT BELIEVE THAT IT CAUSED ME TO MISS A SUBSEQUENT CLRNC. WHEN THE F/O FINISHED BRIEFING THE PAX; HE SWITCHED THE #1 RADIO TO THE LAX TWR; BUT COULD NOT LET THEM KNOW WE WERE ON FREQ AS IT WAS TOO BUSY. THE VECTOR WAS TAKING US THROUGH THE FINAL APCH COURSE TO RWY 24R; AND I URGENTLY REQUESTED THAT HE CLARIFY WITH THE TWR IF WE WERE TO INTERCEPT THE LOC OR WERE CLRED FOR A VISUAL APCH. HOWEVER; BECAUSE OF FREQ CONGESTION; WE COULD NOT GET THEIR ATTN. AT THAT TIME; WE HEARD THE CTLR AND ANOTHER PLT DISCUSSING THE SMT INTRUDING INTO THEIR FLT PATH. TWR ISSUED INSTRUCTIONS FOR ME TO MAKE AN IMMEDIATE RIGHT TURN; WHICH I DID; AND LANDED ON RWY 24R. ON CONTACTING GND; I WAS GIVEN A PHONE NUMBER FOR APCH CTL. I CALLED AND SPOKE WITH THE SUPVR AND EXPLAINED WHAT HAD HAPPENED. HE SEEMED SATISFIED; AND ASSURED ME THAT NO ACTION WOULD BE TAKEN AGAINST MY PLT CERTIFICATE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: FREQ WAS VERY CONGESTED AND RPTR FELT WAS BTWN ROCK AND HARD PLACE; KNEW HAD TO TURN BUT WAS NOT CERTAIN THAT WAS WHAT APCH WANTED. DURING CALL WITH SUPVR OF TRACON; GET IMPRESSION THEY HAD GIVEN TURN AND PROBABLY INTERCEPT; BUT ALSO REALIZED THEY HAD NOT RECEIVED ACKNOWLEDGEMENT AND IT WAS THEIR PROB AND REASON TO ASSURE RPTR NO ACTION WOULD BE TAKEN AGAINST HER PLT CERTIFICATE.