Question

When a vector is lying at x-axis, its y-component is

Answer 1

By stating that the force vector is along the y axis, you’ve implicitly said that there is no x component.

If you want to get more technical, then you take a unit vector along the x axis and multiply it by the magnitude of f times the cosine of the angle between the x axis and the y axis. That angle is 90 degrees by definition, so the cosine is 0, and thus the magnitude of the vector is zero.