A method is presented for localizing acoustic sources using an array of sensors, the output of each being a vector consisting of the acoustic pressure and acoustic particle velocity. We derive a compact expression for the Cramer-Rao bound (CRB) on the estimation errors of the source direction-of-arrival (DOA) parameters in the multi-source multi-vector-sensor model. An explicit expression is found for the mean-square angular error (MSAE) bound for source localization with a single vector sensor. We present two simple algorithms for estimating the source DOA with this sensor, along with their statistical performance analyses.