UNAUTH TKOF BY PLT AND PAX IN A PA44 AFTER CTLR ISSUES A DEP HDG AT HEF; VA.

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MY TRAINING (PIC) PARTNER AND I (PNF) WERE HOLDING SHORT ON TXWY B FOR DEP ON RWY 34R. SHORTLY AFTER RECEIVING THE HOLD SHORT INSTRUCTIONS; THE TWR CALLED US AND TOLD US TO FLY A PARTICULAR VECTOR. I CANNOT REMEMBER THE ALT; BUT I BELIEVE THE HDG WAS 270 DEGS. CTLR DID NOT SAY TO TAXI INTO POS AND HOLD. WE VISUALLY CHKED FOR TFC ON FINAL; AS WE ALWAYS DO BEFORE TAXIING ONTO A RWY; AND FINAL WAS CLR. WE THEN TAXIED ONTO THE RWY; SAW THAT THE RWY WAS CLR OF OTHER TFC; AND TOOK OFF. UPON REACHING AN ALT OF ABOUT 500 FT AGL; THE TWR CTLR CALLED AND TOLD US THAT WE HAD NOT BEEN CLRED FOR TKOF. BOTH MY PARTNER AND I WERE SHOCKED. WE BOTH THOUGHT THAT WE WERE CLRED. HOWEVER; RECOGNIZING THAT THIS WAS NOT AN APPROPRIATE TIME TO INITIATE A DISCUSSION WITH THE TWR OVER WHAT HAD HAPPENED; I APOLOGIZED. CTLR CALLED A SECOND TIME TO TELL US WE WERE NOT CLRED. I DO NOT KNOW WHY; BUT THEN I TOLD CTLR THAT I UNDERSTOOD (BASED ON THE FIRST CALL) THAT WE WERE NOT CLRED. AS WE FLEW TO OUR DEST AND AFTER OUR ARR; WE DISCUSSED THE SIT AND MENTIONED THAT WE WOULD LOVE TO HEAR THE RECORDING. WE ARE STILL NOT SURE THAT WE DEPARTED WITHOUT A TKOF CLRNC.