we can define cross products mathematically like if we take two vectors then we can find another vector with certain properties but why do we use it in physics, if we consider a hypothetical physical quantity like a force which is equal to cross product of certain vectors (example force on a charge in motion in an uniform magnetic field ) why is it so? why does that force have to be a cross product of two vectors?Is it possible to come up with them when what we do is just observe nature?then how?

We can define cross products mathematically like if we take two vectors, we can find another vector with certain properties but why do we use it in physics, if we consider a hypothetical physical quantity like force which is equal to cross product of certain vectors?

For example, the force exerted on a charge in motion in an uniform magnetic field.

Why is it so? Why does that force have to be a cross product of two vectors?

Is it possible to come up with them when what we do is just observe the nature?

we can define cross products mathematically like if we take two vectors then we can find another vector with certain properties but why do we use it in physics, if we consider a hypothetical physical quantity like a force which is equal to cross product of certain vectors (example force on a charge in motion in an uniform magnetic field ) why is it so? why does that force have to be a cross product of two vectors?

we can define cross products mathematically like if we take two vectors then we can find another vector with certain properties but why do we use it in physics, if we consider a hypothetical physical quantity like a force which is equal to cross product of certain vectors (example force on a charge in motion in an uniform magnetic field ) why is it so? why does that force have to be a cross product of two vectors?Is it possible to come up with them when what we do is just observe nature?then how?