[shadowdaone]

The vibrational modes of XeF2 are at 555, 515, and 213 cm-1 but only two are IR active.
Explain why this is consistent with XeF2 having a linear structure.

From what I know, since it has 3 atoms it should have 3*n - 5 vibrational modes, thus 3*3 - 5 = 4 modes. Yet the problem tells me it only has 3, which would suggest a non-linear shape. How to explain this?

[Corribus]

There are two things the problem is trying to get you to think about. First, why are there only three modes instead of your predicted four, and why are only two of those modes IR active?

To address the first question: you say there are four vibrational modes anticipated. This is correct. Now, can you state what they are?
To address the second question: what is the criterion for a vibrational mode to be IR active?