A C172 DEPARTING ON AN IFR FLT PLAN DEVIATED FROM A VECTOR HDG AND FLEW TOWARD DEPARTING TFC.

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I UNDERTOOK A PLEASURE FLT FROM ZZZ TO ZZZ1 WITH 1 PAX. THE WX WAS CLR AND VMC. BECAUSE THE GPS IN THE ACFT I WAS USING HAD AN EXPIRED DATABASE; I PLANNED TO USE 2 ONBOARD VOR RECEIVERS FOR PRIMARY NAV AND THE GPS FOR BACKUP. I FILED AN IFR FLT PLAN FOR A CESSNA '172/U.' THE INITIAL PART OF MY FLT PLAN WAS ZZZ TO THE INTXN; THENCE V97 TO THE ZZZ4 VOR. I SET ONE VOR RECEIVER TO THE VOR AND THE SECOND TO THE ZZZ4 VOR. I SET THE GPS TO INDICATE A DIRECT TRACK BTWN ZZZ AND THE INTXN. THE DUATS FLT PLAN I PRINTED OUT THAT MORNING INDICATED A HDG OF 017 DEGS TO THE INTXN. THE L-22 IFR ENRTE LOW ALT CHART DEPICTS THE INTXN AS BEING LOCATED ON THE 350 DEG RADIAL OF ZZZ3 AND THE 174 DEG RADIAL OF ZZZ4. I WAS CLRED 'AS FILED' TO ZZZ1. I WAS CLRED FOR TKOF ON A HDG OF 360 DEGS FROM THE A1 INTXN OF RWY 4. AN AIRLINER WAS HOLDING NEAR THE THRESHOLD OF RWY 4; CLR OF A CONSTRUCTION AREA. AFTER CHANGING FREQS FROM TWR TO DEP; I WAS INSTRUCTED TO INTERCEPT THE 335 DEG RADIAL OF ZZZ3 AND CLB TO MY ENRTE ALT OF 6000 FT. I DIALED IN THE 335 DEG RADIAL OF ZZZ3 AND AFTER A BRIEF TIME TURNED TOWARD A HDG OF ABOUT 050 DEGS TO INTERCEPT THE RADIAL. THE CTLR ASKED WHY I HAD TURNED AND DEMANDED TO KNOW WHETHER I HAD UNDERSTOOD HIS INSTRUCTION TO FLY A HDG OF 360 DEGS TO INTERCEPT THE 335 DEG RADIAL OF ZZZ3. HE SAID MY TURN WAS TAKING ME TOWARD DEPARTING TFC. I APOLOGIZED FOR MY MISUNDERSTANDING AND COMPLIED WITH THE NEW INSTRUCTION TO TURN TO A HDG OF 270 DEGS UNTIL TFC WAS CLR OF THE AREA. I DID NOT INTENTIONALLY IGNORE THE CTLR'S INSTRUCTIONS. ALTHOUGH THE DEP HDG I WAS INITIALLY ASSIGNED WAS 360 DEGS; I THOUGHT -- MISTAKENLY; IT NOW APPEARS -- THAT I WAS CLRED TO TURN TO A HDG THAT WOULD INTERCEPT THE 335 DEG RADIAL MORE PROMPTLY AFTER I WAS TOLD TO INTERCEPT THAT RADIAL. IN THE FUTURE; I WILL PROBABLY ASK FOR VERIFICATION OF A CLRNC BEFORE I TURN TOWARD AN ASSIGNED RADIAL. I TRIED TO PLAN THIS FLT CAREFULLY; BUT APPARENTLY MY SITUATIONAL AWARENESS LAGGED BEHIND THE INSTRUCTIONS I RECEIVED DURING CLBOUT.