Euler equations with an auxiliarty condition

Euler equations with an auxiliarty condition - shortest path, Mathematics

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1. Finding the shortest path btween any two points on the surface of a sphere but use the method of the euler equations with an auxiliarty condition imposed?

Question2:

Find the shortest path between the (x,y,z) points (0,-1,0) and (0,1,0) on the conical surface z=1-(x²+y²)^1/2 what is the length of the path?

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