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Lets apply what we learned in the last video into a concrete example of the work done by a vector field on something going through some type of path through the field. So lets say that I have a vector field. Its defined over r2 for the x-y plane. So its a function of x and y. It associates a vector with every point on the plane. And lets say my vector field is y times the unit vector i minus x times the unit vector j. And so you can imagine if we were to draw-- lets draw our x- and y-axes. Ill do it over here. If we were to draw our x- and y-axes, this associates a vector, a force vector-- lets say this is actually a force vector-- with every point in our x-y plane. So this is x and this is y. So if were at the point, for example, 1, 0, what will the vector look like thats associated with that point? Well, at 1, 0, y is 0, so this will be 0, i minus 1, j. Minus 1, j looks like this. So minus 1, j will look like that. At x is equal to 2-- Im just picking points at random, on
