The rms velocity of molecules of a gas at temperature T is vrms. Then the root mean square of the component of velocity in any one  particular direction will be

Let velocity of any molecule = vxi^+vyj^+vzk^Root mean square velocity = vx2+vy2+vz22vrms=vx2+vy2+vz2But probability of motion in all directions is the same, so vx=vy=vzvrms=3vx2⇒vx=vrms/3Root mean square of the component of velocity in any one particular direction = vx2=vxClearly, required component = vx=vrms/3