Sketch the vector field −→F (x, y) = √ y x2+y 2 −→ı − √ x x2+y 2 −→ by drawing enough vectors at points in the plane to give a sense of the shape of the field. One way to draw a vector field is to select a grid of points, say (m, n) with integers m and n between −3 and 3 (skipping (0, 0) in this example), and drawing the vector −→F (m, n) with its tail at the point (m, n). That sounds like a lot of work, but you should quickly see the pattern that will allow you complete the sketch without a lot of tedious labor.