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As mentioned on this website https://www.studeersnel.nl/nl/document/technische-universiteit-delft/flight-orbital-mechanics-and-propulsion/chapter-05-preliminary-orbit-determination/4604099, we need to use geocentric position for the 3 vectors to get orbital elements. In my case, i have the position vectors defined in an ECEF frame, is it ok to use it as an input or should i convert my positions into ECEI?

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The text you linked tells you what to use, at the bottom of page 3:

the perifocal coordinate system, in which the unit vector p lies in the direction of the eccentricity vector e and w is the unit vector normal to the orbital plane, in the direction of the angular momentum vector h.

Since you need the specific angular momentum, it's easiest to calculate in inertial coordinates. Doing it correctly in Earth-fixed requires extra terms to account for the amount of rotation that became part of the coordinate system. Also note, in the case of three observations taken from the same ground location at three different times, the rotation of the Earth means the starting points of those three vectors will be different in ECI.

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