Basically all that you're doing is taking one vector and putting it on the end of another vector. That is to say that if you have a vector from Payton to the Hancock Building, and a unit vector (we'll call a unit a single block) pointing south, adding the vectors would put you at the Water Tower. So, you're added vector would be the vector from Payton to Water Tower.
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I always just picture a parallelogram with the sum of the vectors as the diagonal.
Basically all that you're doing is taking one vector and putting it on the end of another vector. That is to say that if you have a vector from Payton to the Hancock Building, and a unit vector (we'll call a unit a single block) pointing south, adding the vectors would put you at the Water Tower. So, you're added vector would be the vector from Payton to Water Tower.
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