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,
(t,2t,3) = k(2t,5t,-1)
then
t = 2kt --> k = 1/2
2t = 5kt --> k = 2/5
contradiction, the value of k would have to be the same
no value of t makes them parallel

to be perpendicular, their dot product has to be zero
2t^2 + 10t^2 - 3 = 0
12t^2 = 3
t^2 = 1/4
t = ± 1/2