Please answer! what vitamin is lacking when you have dark elbows and knuckles?

None - Psoriasis?: It is unlikely that this has any relation to any vitamin deficiency. Vitamins= single molecules present in all kinds of foods. Deficiencies, in first world countries with lots of foods available/eaten, are relatively rare (exception vitamin D3 from cholesterol+UV light). Such patterns are not rare; also possibly c/w psoriasis (very variable in presentation; a small possibility).