Determine whether the following statements are true and give an explanation or counterexample.

a. proj_vu = proj_uv.

b. If nonzero vectors u and v have the same magnitude, they make equal angles with u + v.

c. (u • i)² + (u • j)² +  (u • k)² = |u|².

d. If u is orthogonal to v and v is orthogonal to w, then u is orthogonal to w.

e. The vectors orthogonal to (1, 1, 1) lie on the same line.

f. If proj_vu = 0, then vectors u and v (both nonzero) are orthogonal.