So of course the first thing I did was integrated it a few times to get:Show that a curve $\displaystyle \gamma$ such that $\displaystyle \dddot{\gamma} = 0 $ everywhere is contained in a plane

$\displaystyle \gamma (t) = (a_1 t^2 + b_1 t + c_1 , a_2 t^2 + b_2 t + c_2, a_3 t^2 + b_3 t + c_3)$

where the a, b and c's are constants.

Now how do I continue from there?

EDIT:

Actually I think I have it,

The parametric equation of a plane is $\displaystyle \gamma (t) = (a_1 t + b_1 u + c_1 , a_2 t + b_2 u + c_2, a_3 t + b_3 u + c_3)$

where t and u are the varying parameters. In the above integrated equation, there's 2 varying parameters, $\displaystyle t$ and $\displaystyle t^2$ so it almost fits the equation of a plane, but in this case u is restricted to u=t^2