I have $f(x,y) = xy$ which has the Gradient Vector Field F$(x,y) = (y,x)$
I believe the correct way to draw individual vectors is to map points into the formula, for example at point $(1,-3)$ we will have a vector $(-3,1)$
However, drawing this Gradient Vector, we get an image like this
This confuses me because in the image, $(1,-3)$ does not have a vector $(-3,1)$ and also, there are no overlapping vectors. Or is this image taking each individual vector and creating these curves? And if I am simply graphing each individual vector, are they allowed to overlap?
Notice the scale option is at $0.1$: the vector shown is not $(-3, 1)$, but rather $(-0.3, 0.1)$.
This is probably to make it possible to see what is going on in the image.