So far I have figured out everything except the angle alpha of f,g. What I tried was I drew this triangle:
and found side length c by doing dist(f,g) = ||f-g|| = sqrt() and I ended up with c = sqrt(54)
Then I used the law of cosines to find the angle of alpha and got 14.14 degrees but it was the wrong answer.
What is wrong with my approach?
I believe the angle is arccos(| < f, g > | / (||f|| * ||g||)) So assuming your numbers are correct that would be 1.115r or ~64deg