When rendering using cycles the hair mesh overlaps with the face mesh and a black line appears.
How do I get rid of the black line?
Updated: Wire frame view
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Your hair mesh is going inside the face and due to that line is showing while render.
you may edit the hair mesh and pull outside few vertices to remove this line. So while you are in edit mode Edges should look like this:
Updated: Problem area is seems to be here:
These 2 vertices are going under the face mesh.
I cant reproduce the black line though, but here is how it might be issue and fix