Both my kids are determined, though in different ways. Sylvia wants to know why everything is the way it is. If you've spent more than 5 minutes with her you know what I mean. She peppers everyone with questions, from "why do birds lay eggs?" to "why do I have to eat with a fork?" and everything in between. Which is to say, she's both curious and requires an explanation for why she has to do things before she'll do them.
Paul hasn't reached the why stage yet (being non-verbal and all). His determination comes out in other ways, often involving wheeled or circular objects. For example, this morning, after signing time at the library he wanted to move the teacher's wheeled cart around. He would NOT be content with playing with the wheels, or just pushing it back and forth; no, he had to push it to the door for her. Fortunately, once she was out the door he quickly forgot about the cart.
This afternoon he climbed up the child safety gate I put up to keep him out of Sylvia's room during nap time. After dinner he decided he just had to turn the knobs on the washing machine and fussed until I moved a stool over for him to stand on. Once up he was quite happy for some minutes, just rotating the knob. Before bed he did the tupperware sorting toy six or seven times (with much assistance, of course) before getting bored with it, lasting much longer than I did. The kid's got some serious concentration skills already.