The substance that has vibrating particles in regular fixed positions is a solid.

Here's why:

* Solids have a strong intermolecular force holding their particles tightly together. This arrangement gives them a definite shape and volume. The particles are locked in a rigid structure and can only vibrate in place.

* Liquids have weaker intermolecular forces than solids. The particles can move around more freely, leading to a definite volume but not a definite shape.

* Gases have the weakest intermolecular forces. Their particles are far apart and move freely, taking the shape and volume of their container.

Let me know if you'd like to know more about the states of matter!