Observation of enhanced magnetic relaxation due to counterflow and quantized vortices is reported in rotating superfluid3He-B. These phenomena were studied using a novel method based on the homogeneously precessing domain (HPD) mode, characteristic of the B-phase spin dynamics. The additional HPD absorption can be related to the equilibrium vortex structures and, therefore, this method yields information complementary to textural CW-NMR measurements, which are sensitive to the static magnetic properties of vortex cores. Primarily, the HPD method provides a simple and effective means for studying transient processes, e.g., vortex creation in3He-B; a clear difference between axisymmetric and non-axisymmetric vortices was observed.