Let a and b be nonzero vectors in Rn. a) If (t) = a + tb for t R, show that for each to,

Let a and b be nonzero vectors in Rn.
a) If ɸ(t) = a + tb for t ∈ R, show that for each to, t0, t1, t2 ∈ R with t1, t2 ≠ t0, the angle between ɸ(t0) - ɸ(t0) - ɸ(t0) and ɸ(t2) - ɸ(t0) is 0 or π.
b) If θ is the angle between a and b, show that a and b are parallel according to Definition 8.4 if and only if 6 = 0 or n, and that a and b are orthogonal according to Definition 8.4 if and only if θ = 0 or π, and that a and b are orthogonal according to definition 8.4 if and only if θ = π/2.