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Your second solution can be improved by Evaluate[] on the first plot argument. Plot[Evaluate[y /. sol], {x, -10, 10}, PlotLegends -> Automatic]


I am not sure whether the intention is vectors with all positive entries. If not then potential pairs (a,-a) will also be division by zero. Here is another implementation of formula, removing zero denominators: cd[u_, v_] := Module[{pos, us, vs}, pos = Position[u + v, _?(# != 0 &)]; us = Extract[u, pos]; vs = Extract[v, pos]; Total[(us - ...

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