Question

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?

a) You can end up at your starting point if the vectors A and B have the same magnitude.

b) Two nonzero vectors can add to give zero only if they have opposite directions.

c) Two nonzero vectors can add to give zero if they have the same direction.

d) The maximum distance you can end up from the starting point A+B is always greater than the sum of the lengths of the two steps.

Answer 1

You end up at your starting point if displacements A and B are equal in magnitude but opposite in direction. Two vectors add to give zero under these conditions. The maximum distance with vector addition occurs when the vectors are in the same direction.

Step-by-step explanation:

Under what circumstances can you end up at your starting point after taking two steps A and B? This scenario occurs when the two nonzero displacement vectors A and B are of equal magnitude but in opposite directions.

In vector terms, two nonzero vectors can add to give zero if and only if they have equal magnitudes but are 180 degrees apart in direction, effectively cancelling each other out. Regarding the maximum distance you can end up from the starting point after displacements A and B, the maximum distance is indeed the sum of the lengths of the two steps, but only when the vectors are in the same direction. If the vectors have opposite directions, the maximum distance would not be greater than the sum of the lengths; it would be zero.