Are vitamins FDA approved

The FDA can withdraw vitamins (and other supplements and foods) only when danger has been proven. What you're likely thinking of is the way the FDA regulates drugs. The difference can be subtle: a claim to cure a specific disease or treat a certain condition makes something a drug instead of a supplement. For example, if your pill says it will "improve heart function," it's considered a supplement, but if it says "improve hypertension," it's considered a drug. DRUGs are highly regulated by the FDA and often take years, 100's of millions of dollars in trials to prove safety and efficacy, and literally truckloads of paperwork. You or I could sell a SUPPLEMENT we made in our garage tomorrow and the FDA would have no legal power to regulate us. As I see it.

UPDATE:

FDA's attitude towards and regulations covering dietary supplements have changed in recent years. They definitely do regulate dietary supplements [DS] and one can look up many Warning Letters to DS firms. Check out "21 CFR 111" for the current regulations. Some of the requirements treat DS more like drugs, although they come under CFSAN (Center for Food Safety and Nutrition).

Do not try making DS in your garage. FDA has the authority to shut you down.