This is a wonderful, tricky question, a paradox of sorts (as you probably realize).
Without reason, we could not ask or answer this question. Without love, we could ask or answer but would lack the drive to do so. I’m assuming you mean more than just Agape love here and include the Eros, Philia, and Storge. If you include these, then without love, there would be no motive for being. It’s love (of others, learning, self, creating, …) that drives us.
Reason provides the framework in which we create our world. Love provides the push (or pull) that keeps us moving, creating, destroying, and otherwise changing the world. Without love, we might exist and even have a reason-like framework, but we would not be alive in the same sense as a human being, driven by desire. Without reason, we might exist physically, but we would be unaware of it because we’d lack a means of creating a framework for understanding. Buddhism has something to say about this, but that’s a whole new thread … 🙂
I’d like to hear your opinions on this.