Michael J. answered 08/12/15
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Effective High School STEM Tutor & CUNY Math Peer Leader
If you have two vectors going in the same direction, then the distance vector is the resultant vector. You add the distances of each vector. If you have two vectors going in opposite directions, then the resultant vector is the difference between the vectors. If you have two vectors in which one goes vertical, and the other goes horizontal, then the resultant vector is found using the Pythagorean theorem.
Not every distance vector in each case is the shortest path. Therefore, they are not the same.