The vibrational modes of $\ce{XeF2}$ are at 555, 515, and 213 cm-1 but only two are IR active. Explain why this is consistent with $\ce{XeF2}$ having a linear structure.
From what I know, since it has 3 atoms it should have 3n - 5 vibrational modes, thus 33 - 5 = 4 modes. Yet the problem tells me it only has 3, which would suggest a non-linear shape. How to explain this?