Are the projections of the same force on two parallel axes equal? Are the projections of the same force on two parallel axes equal? If the projections of two forces on the same coordinate axis are equal, are the two forces necessarily equal? Seeking reasons

Are the projections of the same force on two parallel axes equal? Are the projections of the same force on two parallel axes equal? If the projections of two forces on the same coordinate axis are equal, are the two forces necessarily equal? Seeking reasons

The first problem: it's equal
Second question: not necessarily equal
reason:
The projection of the force on the coordinate axis is f × cosa, and a is the angle between the force and the coordinate axis
If the two coordinate axes are parallel to each other, the angle a between the force and the coordinate axis is equal, so the projection f × cosa is equal
The projection of two forces on the same coordinate axis is equal, that is F1 × cosa1 = F2 × cosa2. If A1 ≠ A2, then F1 ≠ F2