Is force or field decomposition into component vectors always valid?
Lets say a constant electric field $\vec{F}$ is acting in space such that it makes an angle $\phi$ with respect to the horizontal direction. The component along x axis (horizontal direction) is $F\cos(\phi)$ and along the vertical $F\sin(\phi)$. Is there any assumption that the space is homogeneous or any other such (uniform space) condition while applying decomposition?
OR is it like decomposition of vectors always refers to a single point in space, and doesn't matter upon the nature of medium/space?
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