EPS file?

Yes, if it is correctly formatted. I have seen all manner of files simply 'saved as' .EPS, which of course is not the same as a true vector file.
 
It can be a vector file yes, if it is vector then it will be able to be scaled/re-sized.

But you can also save bitmap files as .eps, they wouldn't be able to be re-sized.
 
You could try opening it in a text editor. PostScript should be human-readable (but not necessarily understandable!)
Alternatively, the PostScript interpreter GhostScript is free software that should be able to render the output of the file for you.
 
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