does it necessarily follow from dr/dt = ar(t) that r(t) must trace out a straight line through the origin? r(t) is a vector function and 'a' is a scalar constant.

i have a counterexample: r(t)={2exp(at), 3exp(at)}. r(t) cannot be {0, 0} because of properties of exp(at).

this is a qustion in a calculus book. so i am assuming i am missing something by finding a counterexample.