One method to get orthogonal vectors and then orthonormal vectors from a vector is to use Gram-schmidt process. For complete process of Gram-Schmidt see "Linear Algebra and Its Applications" by Gilbert Strang.
let U1=a i+b j + c k
where a , b , c are known
to get a vector U2 orthognal to it
then let U2=x i+ y j+z k
where (x+a)+(y+b)+(c+z)=0
this is one equation in three variable whch means infinite solutions which is true