Hello,

I'm not sure what you're trying to get ?

Did you prove that it was an orthonormal basis ?

If you're looking for and , then... :

Because the scalar product is bilinear, this is equal to :

But . Here, because it's an orthonormalbasis.

And because it's anorthonormal basis.

Therefore,

If you prefer, the scalar product of y with the n-th vector of an orthonormal basis represents the n-th coordinate of y in this basis. (this is extra info and I'm not sure I explained it well )