Question

draw the vector field F=xi+yj at sampling points on the circle x^2+y^2=1

Answer 1

You can conduct an experiment.

1) Go find some little kid's ROUND swimming pool.
2) Make sure it's on a level surface.
3) Fill it with water.
4) Suddenly remove ALL the walls - simultaneously.

Where will the water go? Will it go one direction more than another. Will some direction go faster than another?

Note: I do not actually recommend destroying little kid's (or anyone else's) personal property OR making them cry.

Answer 2

all should have unit length.