The state of matter where atoms vibrate but remain in a fixed position is solid.

Here's why:

* Solids have a definite shape and volume. The atoms are tightly packed together in a regular, repeating arrangement called a crystal lattice. While they vibrate, they are held in place by strong intermolecular forces.

* Liquids have a definite volume but take the shape of their container. Their atoms are closer together than in gases but have more freedom to move around.

* Gases have no definite shape or volume. Their atoms are far apart and move freely in all directions.

Let me know if you have any other questions!