Here is an study problem for my final exam tomorrow:

a) Find an orthonormal basis for R3 that includes a vector parallel to

(0, 3, 4)Transpose.

b) Find the representation of (3, 0, 4) with respect to your basis from a).

c) Verify Plancherel's formula for this vector using this representation.

I am pretty sure I can do part c), but I want to make sure I get everything correct up to that point. Any help is much appreciated. Thanks in advance!