I'm having trouble understanding the use of Vector in machine learning to represent a group of features.
If one looks up the definition of a Vector, then, according to wikipedia, a Vector is an entity with a magnitude and direction.
This can be understood when applying Vectors to for example physics to represent force, velocity, acceleration, etc...: the components of the Vector represent the components of the physical property along the axes in space. For example, the components of a velocity vector represent the velocity along the x, y and z axes
However, when applying Vectors to machine learning to represent features, then those features can be totally unrelated entities. They can have totally different units: one feature can be the length in meters of a person and another can be the age in years of the person.
But then what is the meaning of the Magnitude of such a Vector, which would then be formed by a summation of meters and years? And the Direction?
I do know about normalization of features to make them have similar ranges, but my question is more fundamental.