Get mapping postion of 1 point on a plane defined by 3 points

Hi, I'm beginner in Unity 3D, so please forgive me if I ask something sounds silly.

I have 5 vectors as below:

• Vector normal (like transform.up but customized).

• Vector right (like transform.right).

• Vector forward (like transform.forward, but was created by using Vector3.Cross(vectorRight, vectorNormal) ).

• Vector lookat (my character is looking along this vector).

• Vector finalLookat (but I need my character look along this vector as the final result).

• Plane1(is defined by 2 vectors right and forward).

• Plane1 area(area which can be reached by expanding plan1, finalLookat point may lies on this area when it goes out of plan1 since vector lookat will rotate all the time).

Because of customizing of 2 vectors normal and forward, vector lookat used to, but no more be the right vector I planned to create.

Please help me to create the vector finalLookat, thank a lot.