  In the previous two papers, namely, \citet{anuknn11} and \citet{anuetal11} we
solved the polarized radiative transfer (RT) equation in multi-dimensional
(multi-D) geometries, with partial frequency redistribution (PRD) as the
scattering mechanism. We assumed Rayleigh scattering as the only source of
linear polarization ($Q/I, U/I$) in both these papers. In this paper we extend
these previous works to include the effect of weak oriented magnetic fields
(Hanle effect) on line scattering. We generalize the technique of Stokes vector
decomposition in terms of the irreducible spherical tensors $\mathcal{T}^K_Q$,
developed in \citet{anuknn11}, to the case of RT with Hanle effect. A fast
iterative method of solution (based on the Stabilized Preconditioned
Bi-Conjugate-Gradient technique), developed in \citet{anuetal11}, is now
generalized to the case of RT in magnetized three-dimensional media. We use the
efficient short-characteristics formal solution method for multi-D media,
generalized appropriately to the present context. The main results of this
paper are the following: (1) A comparison of emergent $(I, Q/I, U/I)$ profiles
formed in one-dimensional (1D) media, with the corresponding emergent,
spatially averaged profiles formed in multi-D media, shows that in the
spatially resolved structures, the assumption of 1D may lead to large errors in
linear polarization, especially in the line wings. (2) The multi-D RT in
semi-infinite non-magnetic media causes a strong spatial variation of the
emergent $(Q/I, U/I)$ profiles, which is more pronounced in the line wings. (3)
The presence of a weak magnetic field modifies the spatial variation of the
emergent $(Q/I, U/I)$ profiles in the line core, by producing significant
changes in their magnitudes.
