This question may sound silly but it is fundamental to me.
Divergence is defined as scalar sum of rate of changes of three components of the vector with respect to the axis. I have difficulty to understand why the 3 components should be added together as scalars (why dot product is used to define divergence)? How to understand this quantity represents net flow out/into that point.
Why divergence is not defined as a vector $$ \frac{\partial F_x}{\partial x}i+\frac{\partial F_y}{\partial y}j+\frac{\partial F_z}{\partial z}k$$