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Compact vector formulas are given for the great ellipse on the spheroid providing vector solutions to both the forward and the inverse problems and conversions of longitude and latitude. The solution incorporates a closed form for the azimuth and the derivation of this equation is presented and illustrated. This paper also shows that a computer algebra system and linear algebra are powerful tools to solve some mathematical derivations that may be useful in navigation, geodesy, and cartography.

The vector solutions for the great ellipse on the spheroid