Let A(t) = f1(t)i + f2(t)j and B(t) = g1(t)i + g2(t)j, t ∈ [0, 1], where f1, f2, g1, g2 are continuous functions. If A(t) and B(t) are non-zero vectors for all t and A(0) = 2i + 3j, A(1) = 6i + 2j, B(0) = 3i + 2j, B(1) = 2i + 6j, show that A(t), B(t) are parallel for some t.