Given vectors u= (t, 2t, 3) and v=(2t, 5t, -1). For what values of t

Question

a) are u and v parallel?
b) are u and v perpendicular?

Answer 1

to be parallel u = kv
or in our case: 2t/t = 5t/2t = -1/3
or
2/1 = 5/2 = -1/3 which is a contradiction, so
no value of t makes them parallel

to be perp. u•v = 0
2t^2 + 10t^2 - 3 = 0
12t^2 = 3
t^2 = 1/4
t = ± 1/2