If \(\vec{L}\) is the orbital angular momentum operator and \(\vec{\sigma}\) are the Pauli matrices, which of the following operators commutes with \(\vec{\sigma} \cdot \vec{L}\)?
1
\(\vec{L}-\frac{\hbar}{2} \vec{\sigma}\)
2
\(\vec{L}+\frac{\hbar}{2} \vec{\sigma}\)
3
\(\vec{L}+\hbar \vec{\sigma}\)
4
\(\vec{L}-\hbar \vec{\sigma}\)