Calculus of vector-valued Help Please.....10 pts for best answer?

1.) A fighter plane which can only shoot bullets straight ahead, travels along the path
r(t) = < 6 - t, 20 - t^2, 2 - t^3/28 >.
(a) Show that there is precisely one time t at which the pilot can hit a target located at the origin.

2.) Show that w(t) = < sin(3t+4) , sin(3t-2) , cos 3t > satisfies the differential equation w'' (t) = -9w(t).