MLG FLC TAKES UP WRONG HDG WHEN ISSUED VECTOR BY APCH CTL. TCASII ACTIVATES.

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WE WERE AT 6000 FT MSL BEING VECTORED BY NEWARK APCH CTL ON A HDG OF 150 DEGS. THE CTLR WAS EXTREMELY BUSY; HE WAS DOING ALMOST NON STOP TALKING. HE GAVE US A L TURN TO WHAT I THOUGHT WAS 110 DEGS. ON THAT HDG WE SOON NOTICED A TCASII TARGET AT OUR ALT AND CLOSING AT ABOUT 3 MI. MY FO SAID 'I THINK HE GAVE US 010 DEGS' AS HE VERIFIED THE HDG (HIS HDG POINTER WAS ON 010 DEGS). I STARTED A L TURN AND CONTINUED A 30 DEG LEVEL TURN AS THE CTLR REISSUED A 010 DEG HDG. TFC WAS GOING BEHIND US NOW AND WE WERE GETTING TCASII WARNING (ALERTS) THEN ADVISORIES. FIRST WAS 'MONITOR VERT SPD' FOLLOWED BY CLB; CLB. AT THE SAME TIME I COULD HEAR THE CTLR TELLING US TO DSND. IT WAS PRETTY NOISY IN THE COCKPIT. A BIT CONFUSING TOO WITH ALL THAT CONFLICTING INSTRUCTIONS. AS SOON AS I RECEIVED 'CLR OF CONFLICT' I DSNDED TO 5000 FT. I CERTAINLY HAD THE WRONG HDG. WITHOUT TCASII I DON'T THINK I WOULD HAVE CAUGHT THE ERROR SOON ENOUGH TO HAVE AVOIDED A NEAR MISS. TCASII IS A GREAT TOOL. I'M SURE THAT PART OF MY MISREADING THE HDG WAS MY EXPECTATION THAT THE VECTOR WOULD HEAD US TOWARD THE ARPT NOT TO THE N. LISTEN; DON'T ASSUME ANYTHING IN A BUSY CTL AREA.