Sometime, the cooking utensils can be damaged by minerals in the food and cause some rust. Would it be wise to use vinegar to remove rust for cooking utensils or are there are better methods?
Vinegar wouldn't be harmful. The resulting reaction would create a ferrous salt which would be easily washed away. However, it was probably the vinegar and other acids in your food that cause the rust in the first place. Steel items stored in a acidic environment rust faster than those in plain water. Washing and storing dry is the best way to prevent rust.
If you want to clean rust from steel utensils, I recommend Barkeeper's Friend. I find it works well on stainless steel … not so well on carbon steel.
And always rinse with water and dry by hand to ensure no rust in the future.