We report on a direct measurement of the pairwise antisymmetric exchange interaction, known as the Dzyaloshinsky-Moriya interaction (DMI), in a Nd^{3+}-doped YVO_{4} crystal. To this end, we introduce a broadband electron spin resonance technique coupled with an optical detection scheme which selectively detects only one Nd^{3+}-Nd^{3+} pair. Using this technique we can fully measure the spin-spin coupling tensor, allowing us to experimentally determine both the strength and direction of the DMI vector. We believe that this ability to fully determine the interaction Hamiltonian is of interest for studying the numerous magnetic phenomena where the DMI interaction is of fundamental importance, including multiferroics. We also detect a singlet-triplet transition within the pair, with a highly suppressed magnetic-field dependence, which suggests that such systems could form singlet-triplet qubits with long coherence times for quantum information applications.