[Tenchi Universe] How and why did Ayeka fall in love with Tenchi?

So I'm re-watching Tenchi Universe for the umpteenth time again and something dawned on me. The relationship between Ayeka and Tenchi seems improbable at best. Like how did she fall for him?

I totally understand how Ryoko fell for him. Life is really nothing but a game to her. She's totally carefree. Ayeka, however, is the responsible one. The polar opposite of Ryoko. While Ryoko is spontaneous, Ayeka is reserved. Ryoko has an aggressive personality, and she's always pulling Tenchi towards her. But Ayeka is subtle. I'm finding that I'm having a hard time being convinced that Ayeka's pursuit of Tenchi isn't artificial-- only the fact that Ryoko and Ayeka are rivals being the reason why Ayeka is "attached" to Tenchi. The entire relationship seems forced, just to manufacture a love triangle.

Maybe I just haven't watched enough, or have forgotten some critical facts about the pairing, but I'm having a hard time with it. And this is coming from somebody who was totally obsessed with Ayeka when I first discovered Tenchi Universe.... back some twenty years ago.