I have the most random hair growing out of my upper cheek, below my eye. Being female, my facial hair doesn’t generally grow much and remains downy.
Now, it’s only one hair, and it’s about 3/4 of an inch long. It’s been there a few days that I’m aware of, and it’s been the same length the whole time. I’ve had one of these before (that I know of. It was growing out of my face too, but I’m not sure if it was in the same spot or not), and have known someone who had one growing out of his upper arm that was about 2-2.5 inches long, so I know it’s not just me.
I don’t really want to pluck it. I guess I’m cultivating it. 
I want to see how long it will grow.
Can anyone explain this to me? Is it just a random cell mutation that produces one spurt of hair growth, and then stops, or what?
It is a good question. I think it happens to most people. I have random hairs that grow out of moles sometimes. That isn’t so unusual. However, I have found dark, rather thick single hairs sprouting from freckles a number of times. They were pretty long as in an inch or more but they were in places that I would have surely noticed in the time that it takes to grow an inch-long regular hair. Do some of those hairs generate in a matter of days or faster?
I’ve never noticed them until they’re fairly long. I’m keeping track of this one to see if it continues to grow for that matter.
These hairs (the two on my face, the one on my friend’s arm) were never sprouting out of moles/freckles. Perhaps it was such a small cluster of melanin that it wasn’t visible to an unaided eye.
If you’ve only noticed it since a few days, you can’t yet tell whether it’s still growing or not. My bet is it’s been growing at normal hair-rate (~.25" a month IIRC) and you’ve only just noticed it. And that it will continue to grow at that rate until it breaks, it falls out or you pluck it.
OK, so I didn’t RC. Nevertheless the point stands; your anomalous hair is (now only) 6 weeks old and you just noticed it.