What will happen if we mix egg yolk and vinegar and oil?
You make mayonnaise.
Mayonnaise is an emulsion; a mixture of 2 or more liquids that are normally immiscible. Here, we take egg-yolks, an aqueous solution, and emulsify it with oil. Home-made mayonnaise made with real eggs, and vinegar, and nice oil, and loads of pepper and salt and mustard is rather nice, and is a good and tasty chemistry experiment you can do in your kitchen.
A really disgusting tasting mixture called mayonnaise.
Under normal conditions, egg yolk and vinegar would not mix. However, the will mix if you add an emulsifier--basically something that prevents them from separating. In this case, the emulsifier would be egg yolk. Once you add the egg yolk, it will take a lot longer for the vinegar and oil to separate. So what do you get? A really cool science lesson and an awful tasting concoction. Seriously, don't eat it. Just don't.