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These formulae describe the high side unit vector and the lateral unit vector from which we can derive the axes vectors when sitting at any given toolface from high side:
If we describe the Earth vector in terms of a north, east and vertical component we can calculate theoretical readings for each axis using the vector dot product. If the Earth's magnetic Field Vector os Mag N, Mag E, Mag V and the Earth's Gravity Field Vector is Gn, Ge an Gv we would expect each sensor to read the vector dot products as follows;
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