Sphere line picking is the selection of pairs of points corresponding to vertices of a line segment with endpoints on the surface of a sphere. n random line segments can be picked on a unit sphere in the Wolfram Language using the function RandomPoint[Sphere[], {n, 2}]. Pick two points at random on a unit sphere. The first one can be placed at the north pole, i.e., assigned the coordinate (0, 0, 1), without loss of generality.
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