My dad has eczema is this hereditary? Can it be passed down to me as well?

Yes. If you have a close relative with allergic dermatitis it increases your risk for getting an allergic disease such as atopic (allergic) dermatitis.
Possibly. I'm sure there is a genetic component to eczema; as well as most everything else. Whether or not you receive it; and whether or not it becomes "active" in you is up to your genes and the environment around you. If you start developing a rash please see you doctor.