It is a false statement i.e. drift velocity is not same in the direction as the applied force.
Drift velocity of a current-carrying conductor can be explained as, the charges i.e. electrons do not flow in the same direction of current. In other word, in most cases the movement of the electrons is almost random, with a small net velocity. So that , the drift velocity, in the direction opposite to the electric field.
Drift velocity 
is inversely proportional to the number of electron per unit volume of the conductor e. Therefore, the formulation can be given as ,
= σ E/ne
The above equation shows the drift velocity in a current carrying conductor
where, is drift velocity , σ is the conductivity, E is electric force and n is number of electrons per unit volume of the conductor e.
Hence here we can say that, the drift velocity is not in the same direction as the applied force.
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