What essential vitamins would a person be missing by leaving out vegetables?

Folate, (folic acid)phytonutrient: It's possible to get most essential vitamins from animal foods, fruits, nuts ; grains with the possible exception of folate (folic acid) (but that can be gotten from beans).More importantly you would miss phytonutrients like flavonoids, carotenoids ; glucosinolates that are essential for optimal health- see http://www.Ars.Usda.Gov/aboutus/docs.Htm?Docid=4142 you can take vitamins but need to eat phytnutreints.