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 are molecules in all kinds of foods and deficiencies in first world countries, with lots of foods available ; eaten, are relatively rare (with possible exception of vitamin d3). Given skin over the extensor surface of joints, this is a pattern c/w psoriasis, very variable in presentation but a possibility.