Find an orthonormal basis for the vector subspace of
Sketch of work:
Spoiler:
first, you don't need to hide your own work! second, you're right so far. now you just need to apply Gram-Schmidt process. let's give a name to the elements of the basis you found:
now find the set is an orthogonal basis for so you just need to normalize them, i.e. find
then would be an orthonormal basis for