Embraer Captain reported deviating from their assigned heading on departure; resulting in flight towards terrain. ATC issued a low altitude alert and vectors away from terrain.

Narrative

Revenue leg ZZZ to ZZZ1 on Aircraft X. My FO got the clearance and recorded it as runway heading to 1000'; turn right to heading 265 and intercept VXX as filed; climb and maintain 3000'. I took off on runway XX using noise abatement procedures. At 1000' MSL I started a right turn to heading 265 and noticed we were overshooting VXX (ZZZ [VOR] to ZZZZZ). I continued my right turn past heading 265 to re-intercept VXX as my FO contacted departure control. ZZZ [TRACON] immediately issued a low altitude alert and directed a left turn to heading 210. We complied and leveled off at 3000'. He then gave us a right turn to heading 260. The rest of the flight was uneventful. Our actual clearance was climb to 1000' and turn right to heading 265 for vectors onto VXX then as filed; climb and maintain 3000'. He stated that the turn past heading 265 placed us into airspace where the MVA was 3000'; and our altitude at the time was 2300'; so they had to issue a low altitude alert. I speculated that my FO probably confused the word VECTOR" with "VICTOR XX" while getting the clearance. Suggestions: I believe my FO mistook the word "VECTOR" for "VICTOR (XX)" while recording the clearance at ZZZ. I wasn't in the cockpit at the time; so this is my best guess. Lesson learned is that it's the responsibility of the crew to accurately record the departure clearance and query clearance delivery if there is any confusion or questions. My FO is actually a very sharp and competent pilot; but we are all prone to error."