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I understand vectors perfectly, but still something is bothering me when it comes to forces being represented as vectors

We'd compute the x component of force F with F*cos(alpha), alpha being angle force has with x axis.

Promblem I have with this is why does force follow the same rules vectors do? Meaning if same force has smaller angle with x axis then x component of force will be greater. Why, unlike vectors, couldn't x axis be smaller or follow some completely different set of rules?

thank you