Calculus

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

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

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  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

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