Unless you are deficient in nutrients or malnourished, adding more vitamins/minerals will not help you. So only if you believe you have gaps in your nutrition should you take a supplement.
Biotin has no proven efficacy in hair growth of healthy individuals [2017]. Biotin deficiency causes hair loss, but there is no data that supplementing biotin promotes hair [2018].
Iron supplementation reverses iron deficiency and induces hair regrowth.
Zinc deficiency is a cause of alopecia (balding) and zinc supplementation causes hair regrowth [2018].