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We examine the mechanical eigenmodes of a quartz tuning fork (QTF) for the purpose of facilitat- ing its use as a probe for multi-frequency atomic force microscopy (AFM). We perform simulations based on the three-dimensional finite element method (FEM) and compare the observed motions of the beams with experimentally measured resonance frequencies of two QTF systems. The com- parison enabled us to assign the first seven asymmetric eigenmodes of the QTF. We also find that a modified version of single beam theory can be used to guide the assignment of mechanical eigen- modes of QTFs. The usefulness of the QTF for multi-frequency AFM measurements is demonstrated through photo-induced force microscopy (PiFM) measurements. By using the QTF in different con- figurations, we show that the vectorial components of the photo-induced force can be independently assessed, and that lateral forces can be probed in true non-contact mode.