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Planar scanning probe microscopy is a recently emerging alternative approach to tip-based scanning probe imaging. It can scan an extended planar sensor, such as a polished bulk diamond doped with magnetic-field-sensitive nitrogen-vacancy (NV) centers, in nanometer-scale proximity of a planar sample. So far, this technique has been limited to optical near-field microscopy, and has required nanofabrication of the sample of interest. Here we extend this technique to magnetometry using NV centers, and present a modification that removes the need for sample-side nanofabrication. We harness this new ability to perform a hitherto infeasible measurement - direct imaging of the three-dimensional vector magnetic field of magnetic vortices in a thin film magnetic heterostructure, based on repeated scanning with NV centers with different orientations within the same scanning probe. Our result opens the door to quantum sensing using multiple qubits within the same scanning probe, a prerequisite for the use of entanglement-enhanced and massively parallel schemes.