. Given vectors u = (3, 7, −2) and v = (1, −3, 4) in R 3, find the following
(a) the dot product u · v. What does it say about the angle between u and v?
(b) the lengths ||u|| and ||v|| of the vectors.
(c) cos θ, where 0 ≤ θ ≤ π is an angle between u and v.
(d) two vectors that have length 5 and are parallel to u.
(e) two vectors that have length 11 and are parallel to v.