Which of the following represents the correct electron configuration for the V^{3+} ion?

Since the ion is $\mathrm{V}^{3+}$, remove 3 electrons from the neutral atom's configuration. Remember that electrons are removed first from the outermost shell, which is the 4s orbital before the 3d orbitals.

Remove 2 electrons from the 4s orbital and 1 electron from the 3d orbital to account for the 3+ charge, resulting in the configuration $[\mathrm{Ar}]\,3d^2$.