  We explore, employing the renormalization-group theory, the critical scaling
behavior of the permutation symmetric three-vector model that obeys
non-conserving dynamics and has a relevant anisotropic perturbation which
drives the system into a non-equilibrium steady state. We explicitly find the
independent critical exponents with corrections up to two loops. They include
the static exponents $\nu$ and $\eta$, the off equilibrium exponent
$\widetilde{\eta}$, the dynamic exponent $z$ and the strong anisotropy exponent
$\Delta$. We also express the other anisotropy exponents in terms of these.
