In this paper we propose architecture of a processor for vector operations involved in on-line learning of neural networks. We target to implement on-line learning on a Radial Basis Function Neural Network (RBFNN) based Face Recognition (FR) system that has pseudo inverse computation as an essential component during training. Synaptic weights of RBFNN output layer need to be updated whenever the FR system comes across a new face to be learnt. For real-time on-line learning, update of synaptic weights is done using an existing Incremental Pseudo Inverse (IPI) algorithm in the place of compute intensive pseudo inverse algorithm. We design a custom data-path for vector operations appearing in IPI algorithm. The custom data-path along with configuration and memory access mechanisms forms a processing unit, termed Processor for Vector Operations (VOP). We simulate and synthesize VOP to target Virtex-6 FPGA using the Xilinx ISE. Apart from on-line learning, the VOPs can be used in acceleration of several applications involving predominant vector-matrix operations.