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In this video tutorial, we learn how to apply the concepts of vector fields by using a concrete example. The vector field is defined in the x-y plane, associating a vector with each point on the plane. The specific vector field discussed is y times the unit vector i minus x times the unit vector j. This vector field represents a force vector at each point in the x-y plane. By selecting random points such as 1, 0 and 2, we can visualize the vectors associated with those points based on the given vector field equation.