r The best way to picture a vector field is to draw the arrow representing the vector, F (x, y), starting at the
point (x, y) . You obviously can’t do it for all points (x, y) , but you get a pretty good idea what the vector fields look like by doing some points.
HW#4: S k e t c h t h e v e c t o r f i e l d ( ) , , F x y x y x = 〈 − 〉 r .
Notice the different length of vectors? What would the length be? How could we represent it?
Why are the vectors along the line y = x all vertical?
These are a pain to do manually. Technology will come in handy here. But that’s all these vector fields are; that’s all they do; start at the given point and draw the corresponding vector.