Finding a mid-angle line between many points

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For any 3 non-colinear points in 3d space (A, B, and Z) there should exist a line/vector M that connects Z to AB where AZM = MZB. image1

I am trying to find a corresponding M for a model with 5 points where none of the points are necessarily coplanar. image2

What would M be here? Does M have to exist? Under what circumstances would it exist?