We study dependence of electromagnetically induced transparency (EIT) resonance amplitudes on the external magnetic field direction in a lin||lin configuration in 87 Rb vapor. We demonstrate that all seven resolvable EIT resonances exhibit maxima or minima at certain orientations of the laser polarization relative to the wave vector and the magnetic field. This effect can be used for development of a high-precision vector EIT magnetometer.PACS numbers: 42.50. Gy, 32.70.Jz, 32.60.+i, 07.55.Ge The ability to measure magnetic field with high precision and good spatial resolution benefits many applications. For example, detection of weak magnetic a field distribution gives a new non-invasive diagnostic method for heart and brain activities, allows identification of defects in magnetizable coatings and films, and can possibly be used for a non-demolishing readout of stored memory domains. Many magnetic sensors available today, such as SQUIDs (superconducting quantum interference devices) [1], spin-exchange relaxation-free (SERF) magnetometers [2,3], and various optical pumping magnetometers [4] are sensitive only to the magnitude of the magnetic field. These magnetometers lose valuable information about magnetic field direction and can allow reduced accuracy due to "heading error" in some systems [5]. The application of coherent optical effects, such as electromagnetically induced transparency (EIT) [6] for magnetic field detection offers exciting perspective for development of high-precision miniature magnetometers [7][8][9][10][11][12]. EIT resonances are associated with the preparation of atoms into a coherent non-interacting (dark) superposition of two metastable states of an atom (such as two Zeeman or hyperfine sublevels of the electronic ground state of an alkali metal atom) under the combined interaction of two optical fields E 0,1 in two-photon Raman resonance in a Λ configuration. The resulting ultra-narrow (down to a few tens of Hz [13,14]) transmission peaks can be used to measure, e.g., a frequency difference between two hyperfine energy levels in Rb or Cs without use of microwave interrogation, making this method particularly attractive for development of miniature atomic clocks [15,16] and magnetometers [10]. In the latter case, the magnitude of a magnetic field can be deduced from the spectral position of an EIT resonance in a Λ link formed between magnetic field-sensitive Zeeman sublevels. However, this method is not sensitive to the direction of the magnetic field vector B.Several publications suggested that the information about B direction can be extracted by analyzing relative intensities of various EIT peaks [17,18]. Yudin et al. [19] showed that a recently studied lin||lin configuration is a promising candidate for EIT atomic clock applications [20][21][22][23]. The amplitude of the magnetoinsensitive EIT resonance is sensitive to the magnetic field direction and has a universal maximum when the laser polarization vector, E, is orthogonal to the plane formed by the magnetic field vector, B,...