Originally Posted by HippieMama
Put some baking soda in the base and mix about a 1/4 cup of white distilled vinegar or pure lemon juice and fill the rest of your base with warm water. It will fizz if you use vinegar once it reacts with the soda. Let it sit in the sink or tub for a few hours. If you don't have a vase brush, just put a small cloth in there and swish it around with some sort of item that is long enough to handle, such as a rubber spatula. Rinse well and let it air dry upside down so the water can drain out. If that doesn't get rid of the line I don't know what will.
It should work, but if it doesn't, pull out the big guns and use CLR. Just be sure to rinse the vase several times afterward.