Question: Sketch the vector field \(\vec{F}(x, y)=\frac{y}{\sqrt{x^{2}+y^{2}}} \vec{\imath}-\frac{x}{\sqrt{x^{2}+y^{2}}} \vec{J}\) 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 \(\vec{F}(m, n)\) 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.

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