Suppose you take two steps a and b (that is, two nonzero displacements). under what circumstances can you end up at your starting point? more generally, under what circumstances can two nonzero vectors add to give zero? is the maximum distance you can end up from the starting point a+b the sum of the lengths of the two steps?

You can end up at the starting point when the steps A and B are equal in magnitude and opposite in directions. The maximum distance you can end up is the sum of A plus B.

Explanation:

Going back to the origin

Dsiplacement is a vector, it means it has a magnitude (value) and a direction. If we take a step to the right (step A), then the only way to go back to the starting point is taking the reverse step (Step B). that is to say taking the same amount of displacement we did on step A but in the opposite direction. If we go to right 4 feet, then we need to go to the left (opposite direction) the same 4 feet.

Maximun distance

As we said, displacement is a vector, so direction is necessary to know how much we have displaced from the starting point. The maximun distance for two steps can be reached when both steps are taken in the same direction. In that scenario distance is equal to sum of  step A and step B.

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