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Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can subsequently interact with any charged particles. EM waves carry energy, momentum and angular momentum away from their source particle and can impart those quantities to matter with which they interact.
Due to this EM waves show electric and magnetic field. An electric and magnetic field have no need a medium to show thier effect. Hence in the presence of electric and magnetic field vector which vibrate perpendeculer to each other and get pertervation EM waves travels in vacuum.