Vitamin E is actually a fat-soluble vitamin, which means it dissolves in fats and oils and is stored in the body's fatty tissues. It plays a crucial role as an antioxidant, helping to protect cells from oxidative damage. The confusion may arise from the phrasing of the question, as it asks for a vitamin that is not fat-soluble. In contrast, vitamins A, D, and K are also fat-soluble vitamins. Therefore, the correct interpretation of the question is that all the listed options are fat-soluble vitamins, and none of them is the correct answer to the question as posed.