Myth or not: Shampoos/Beauty products containing vitamins work as well as actually eating these nutrients?

Shoe Maker asked: What do you think?
Are ingredients in beauty products & shampoos really going to improve your skin if you only put them on the outside of the skin, as opposed to taking actually nutrients internally;
Example- some shampoos and face cremes contain things such as grapefruit extract and vitamin C.
But
does this only help your [...]