Sketch the vector field→− F (x,y) = y √x2+y2→− ı − x √x2+y2→−  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.