And just to double check, you never, ever submit three chapters to agents without having written the rest, right?!
Absolutely. Never, ever, ever. Unless you happen to meet one at a conference or something and they ask to see what you've got so far.
But in general, you only submit when you have a complete manuscript and you have polished it until it gleams. And then given it another polish to be on the safe side.
My agent and I very, very vaguely knew each other because I used to own an independent bookshop and we had a conversation on Twitter after I'd sold it. I said that I was writing, he asked what it was about, I played hard to get and said that it wasn't his sort of thing, he DM'd me and I told him about it and that it was on about 30k and he asked to see it.
So I sent it, he came back with some really useful suggestions and I finished it. He saw it again (when I thought I'd polished as much as I could) and said that he thought it needed still more work. His notes were really helpful. I spent 3 months rewriting it and then he said he loved it and offered me representation.
That is not usual. Finish your manuscript.
Good luck!