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Plane, normal, two points and a triangle

There is a plane. There are two points on the plane (point A and point B). There is a normal to the plane. There is a triangle

Question.
How can a triangle be placed on a plane so that one end is at point A, the other is directed to point B and the vertex is parallel to the normal. The plane is rotated by an unknown degree on all axes.

Hi! Your question is not too clear…mostly for the last part: ‘the vertex is parallel to the normal’
vertexes cannot be parallel to anything…lines can.