How to get the tangent and binormal to a set of coplanar vectors?

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I have a set of vectors A,B,C,D that are colplanar, I have the corresponding normal vector from the cross product of A and B and other additional details to the normal such as its direction cosines. How can I obtain the tangent and binormal vectors to the normal vector

WHAT I TRIED:

  • rotating the normal vector until it became the binormal and tangent in a 3D software at a specific angle for each turned out if I rotated A,B,C,D as an object(or if the vectors A,B,C,D were different but coplanar) the specific angle wasn't constant to get the normal vector to both the tangent and binormal vector positions

  • surfing the web, saw only tangents and binormals with respect to curves. was hoping to see some form of a rotation matrix being applied on the normal vector to give either the tangent or binormal based on the direction cosines of the normal vector since rotating the normal in the 3D software visually solved the problem