Why can vectors (vectors in Physics) be calculated from geometry? How can we prove that everything obeys this law? Why should we abide by this Law and not others?

Vector in Physics
1. They all have size and direction
2. Obey parallelogram rule (triangle rule)
(both of these are indispensable)
((1) the image force has magnitude and direction and obeys the parallelogram rule, so the force is a vector. (2) the image current I has magnitude and direction but does not obey the parallelogram rule, so it is not a vector.)
How to prove it? At the beginning, we thought that the vector in mathematics was derived from the vector in physics
As long as everything is a vector, it must obey this rule. As long as it is a scalar, it will not obey this rule

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