The Gram-Schmidt process will find these vectors for you.

Firstly, the vectors you find will not be unique. Any two perpendicular vectors in the plane can be rotated to find two more.

To find an arbitrary pair of perpendicular vectors, just find another vector that is not a scalar multiple of your normal. You can do this by adding a constant value to one of your components (check that the other two aren't zero -- if they are, then add the constant to one of the zero components). Now that you have this other vector compute the cross product of this vector with the normal to get a vector in the plane. Then compute the cross product between this vector and the normal to get a second vector in the plane - and you are done.

Firstly, the vectors you find will not be unique. Any two perpendicular vectors in the plane can be rotated to find two more.

To find an arbitrary pair of perpendicular vectors, just find another vector that is not a scalar multiple of your normal. You can do this by adding a constant value to one of your components (check that the other two aren't zero -- if they are, then add the constant to one of the zero components). Now that you have this other vector compute the cross product of this vector with the normal to get a vector in the plane. Then compute the cross product between this vector and the normal to get a second vector in the plane - and you are done.