What size is the light? Think the light you’ll get may be inadequate for the space.

Of course you can. But that doesn't mean you will like it. Side lighting is more flattering. Can you have side lighting? Maybe you can't. And then the answer depends on the light selected, the size and the number of bulbs, etc. I bet you could Google how much light is needed over a vanity. This is the first hit I got:

https://www.litelume.com/how-to-determine-bathroom-vanity-light-sizes/#:~:text=Every bathroom is different, so,the light above the mirror.

why not hang it horizontally.

Oh my !! I meant to say horizontal !!! I am so sorry ! Thank you all for your time with this . Forgive me.