Let a and b be nonzero vectors in Rn a) If (t) a tb for t R, show that for each to, t0, t1, t2 R with t1, t2 t0, the angle between (t0) (t0) (t0) and (t2) (t0) is 0 or b) If 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 ...

a Let be the angle between t1 t0 and t 2 t 0 Since t1 t 0 t 1 t 0 b and t 2 t 0 t 2 t 0 b ...

Let a and b be nonzero vectors in Rn. a) If (t) = a + tb for

Question:

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.