LGT CARGO FLT IS VECTORED TOWARD DEPARTING TFC.

Narrative

ON ARR INTO MEMPHIS; APCH CTL TOLD US TO EXPECT RWY 27. COMING FROM THE NE; THIS SEEMED STANDARD.THE APCH CTLR TOLD US TO TURN TO 270 DEG HDG OFF THE ARR; AND TO DSND TO 3000 FT MSL. WE DID. WE LEFT 10000 FT MSL AND STARTED TO DSND TO 3000 FT MSL. ABOUT 8000 FT; THE CTLR TURNED US TO A HDG OF 300 DEG. THIS WAS NOT NORMAL. WE COULD NOT ASK THE CTLR ABOUT THIS NEW HDG DUE TO THE CONGESTED RADIO FREQ WE WERE ON. ABOUT 5200 FT; A DIFFERENT CTLR CAME ON OUR FREQ AND ASKED US TO IDENT; SO WE DID. HE THEN SAID TO MAINTAIN 5000 FT MSL AND TURN TO A HDG OF 180 DEGS. IF WE HADN'T TURNED TO 180 DEGS WHEN THE NEW CTLR STEPPED IN ON THE OLD CTLR; WE WOULD HAVE PROBABLY HIT THE DEPARTING ACFT OFF OF MEMPHIS RWY 36R. BOTH; US AND THE DEPARTING ACFT SAW EACH OTHER THE WHOLE TIME. WE FLASHED OUR LNDG LIGHTS AT EACH OTHER. AFTER LNDG; OUR CREW; DISGUSTED WITH APCH CTL; DECIDED TO FILL THIS RPT OUT. WE PASSED EACH OTHER AT THE SAME FLT ALT; NOT LESS THAN 1500 FT AWAY FROM EACH OTHER. IF WE WERE IMC; IT WOULD HAVE BEEN SERIOUS. WE STILL HAVE NO IDEA WHY THE CTLR VECTORED US TOWARD THE DEPARTING ACFT.