Marketing is the reason vitamins are put in shampoo.
Because they make the shampoo sound like it’s more than just expensive glorified dish detergent.
Although a lot of shampoo brands imply that the various vitamins they put in their products help make hair healthy and shiny, the truth is that vitamins can’t do much of anything for your hair. The hair is already dead, and won’t really absorb or react to anything you put on it.
It’s true that vitamin deficiencies can affect hair, but in that case dull hair is likely going to be the least of your problems.
If daily vitamins (the kind you swallow, of course) are taken regularly, they can help your whole body function better-including the hair follicles that produce hair, but from a scientific standpoint, no nutrients you place on your hair or skin are going to have much benefit.