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I want to transform the origin of a cartesian system. I have a plane (Ax +By +Zc +D = 0) and two perpendicular lines, contained in the plane. I have the equations (parametric) of the two perpendicular lines too. I want to consider these two perpendicular lines as the new coordinates system (the intersection of two lines would be the new coordinates origin: 0.0.0).

I have several points in the planes (defined by using the XYZ coordinates). I need to change the coordinates of these points to the new reference system (X'Y'Z'). In this way I could know in which quadrant of the cartesian system defined by the above lines the points are (this is my final target).

Could anyone help me??? Many many thanks.