 Let's see how an air partial initially at rest achieves geostrophic balance. At rest, the air parcel velocity equals zero, and the only horizontal force acting on the parcel is the pressure gradient force, which has a constant magnitude and direction as long as the pressure gradient remains the same. As soon as the parcel has some velocity, the Coriolis force starts perpendicular into the right of velocity in the northern hemisphere. The Coriolis force begins to move the parcel to the right because the sum of forces on the parcel now has a Y component. Note that the PGF is still always perpendicular to the pressure gradient and the Coriolis force is always perpendicular to the velocity. Eventually, the PGF and the Coriolis force come into opposition with the velocity in between and Coriolis to the right of the velocity. In the end, the Y component of the force is a zero again, so the air parcel remains at the geostrophic velocity.