Final answer:
Two vectors with different magnitudes can add up to zero only if they are antiparallel. For three or more vectors of different magnitudes, they can sum to zero if they form a closed shape. The maximum distance achieved by adding two vectors is the sum of their lengths if they are in the same direction.
Step-by-step explanation:
When dealing with vectors, it is possible for two vectors with different magnitudes to add up to zero if they are equal in magnitude but opposite in direction, making them antiparallel. This is due to the definition of vector addition, which considers both magnitude and direction.
For example, if you take a step of 5 units to the north (vector A) and then a step of 5 units to the south (vector B), you will end up back at your starting point as these two vectors cancel each other out. This can only happen if the two vectors are directly opposite to each other (antiparallel).
However, in the more general case with three or more vectors, they can add to zero even if they have different magnitudes, as long as they form a closed shape like a triangle or a polygon when placed tip-to-tail. The result of adding multiple vectors together in such a manner would be zero, bringing you back to your starting point.
Moreover, the maximum distance you can end up from the starting point when adding two vectors A and B is indeed the sum of their lengths, but only when the vectors are aligned and pointing in the same direction. When they point in opposite directions, the maximum distance will be the difference in their lengths.