a. If r(t) = (at, bt, ct) with (a, b, c) ≠ (0, 0, 0), show that the angle between r and r' is constant for all t > 0.

b. If r(t) = (x₀ + at, y₀ + bt, z₀ + ct), where x₀, y₀, and z₀ are not all zero, show that the angle between r and r' varies with t.

c. Explain the results of parts (a) and (b) geometrically.