The correct answer is A. vector sum of Eb and V.
The net armature voltage of a synchronous motor is the vector sum of the induced voltage Eb and the applied voltage V. The induced voltage is proportional to the speed of rotation of the motor, while the applied voltage is the voltage that is supplied to the motor. The vector sum of these two voltages is the net armature voltage, which is what drives the current in the armature windings of the motor.
Option B is incorrect because the arithmetic sum of Eb and V would not take into account the phase difference between the two voltages. Option C is incorrect because the arithmetic difference of Eb and V would not take into account the magnitude of the two voltages. Option D is incorrect because the vector difference of Eb and V would not take into account the phase difference between the two voltages.