What do you mean by "Vector Field" ? Give any mathematical explanation if possible.?

Question

This question is taken from the "Vector Analysis" of college physics

Answer 1

Any function that has a vector value, or a tuple (x, y, z,....), is a vector field. For a very simple example, the function F(x, y, z) = Vector(x, y, z) generates a vector field, where for every point in 3D space, (x, y, z), there is associated with it the vector(x, y, z), which can be thought of as an arrow rather than a point. If you measured the direction and flow rate of water at different points in a river, using arrows to indicate the flow, then you'd end up with an example of a vector field.

Answer 2

imagine a plane
now imagine vectors all over the plane
yup, a vector field