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We have studied vortex dynamics excited by the spin-transfer-torque effect and find that the direction of the vortex state can be detected electrically using the homodyne voltage signal generated due to the anisotropic magnetoresistance (AMR) effect. An external in-plane dc magnetic field is required to break the cylindrical symmetry in order to obtain a dc response of the homodyne signal. The sign of this rectified voltage changes with the handedness of the vortex state, which makes it a promising method to detect the vortex state electrically. Vortex dynamics is also observed by direct imaging in a scanning transmission x-ray microscope, allowing verification of the measured AMR signal in the correct power and frequency range. The results of micromagnetic simulations are in good agreement with the experimental data. [ABSTRACT FROM AUTHOR]