First find the dot product ~u · ~v of each pair of vectors below. Then find the norms ||~u|| and ||~v||. Finally calculate the angle between each pair of vectors^2 :

(a) ~u = (1, 0, 1) and ~v = (1, −1, 0) ∈ R³.
(b) ~u = (1, −1) and ~v = (−2, 0) ∈ R².
(c) ~u = (1, −1, 0) and ~v = (−2, 0, −2) ∈ R³.
(d) ~u = (2, −1, 0) and ~v = (2, 4, 2) ∈ R³.
(e) ~u = (1, 1) and ~v = (−4, 4) ∈ R².
(f) ~u = (1, 2, 3) and ~v = (−2, 1, 0) ∈ R³.