I have been trying to do this question and I keep getting different to what my lecturer has in the notes. Can anyone please find , and for me?!

The question is:

The equations used in the process are hereApply the Gram-Schmidt orthogonalization procedure to the R-basis to obtain an orthonormal basis for where the inner product is defined by

I dont need the working out, I just want to know the final answers for , and . Thank you!