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Semiconductor nanowires featuring strong spin-orbit interactions (SOI), represent a promising platform for a broad range of novel technologies, such as spintronic applications or topological quantum computation. However, experimental studies into the nature and the orientation of the SOI vector in these wires remain limited despite being of upmost importance. Typical devices feature the nanowires placed on top of a substrate which modifies the SOI vector and spoils the intrinsic symmetries of the system. In this work, we report experimental results on suspended InAs nanowires, in which the wire symmetries are fully preserved and clearly visible in transport measurements. Using a vectorial magnet, the non-trivial evolution of weak anti-localization (WAL) is tracked through all 3D space, and both the spin-orbit length $l_{SO}$ and coherence length $l_\varphi$ are determined as a function of the magnetic field magnitude and direction. Studying the angular maps of the WAL signal, we demonstrate that the average SOI within the nanowire is isotropic and that our findings are consistent with a semiclassical quasi-1D model of WAL adapted to include the geometrical constraints of the nanostructure. Moreover, by acting on properly designed side gates, we apply an external electric field introducing an additional vectorial Rashba spin-orbit component whose strength can be controlled by external means. These results give important hints on the intrinsic nature of suspended nanowire and can be interesting for in the field of spintronics as well as for the manipulation of Majorana bound states in devices based on hybrid semiconductors., Comment: 13 pages, 11 figures