Final answer:
The greatest resultant magnitude when adding two vectors occurs when they are parallel, and the smallest when they are antiparallel; the minimum can be zero if vectors are equal and opposite. The correct answer is b) Greatest: Antiparallel, Maximum: |→A + →B|, Smallest: Parallel, Minimum: 0.
Step-by-step explanation:
When adding two vectors →A and →B, the relative direction between them that produces the resultant with the greatest magnitude is when they are parallel. In this case, the maximum magnitude is the sum of their individual magnitudes, represented by |A + B|.
Conversely, the relative direction that produces the resultant with the smallest magnitude is when they are antiparallel, meaning they are in opposite directions. The minimum magnitude in this case will be the absolute difference of their magnitudes, which can be zero if the vectors are of equal magnitude and directly opposite.
The relative direction between two vectors A and B that produces the resultant with the greatest magnitude is when they are parallel.
The maximum magnitude is obtained when the vectors are added together: |A + B|. On the other hand, the relative direction between the vectors that produces the resultant with the smallest magnitude is when they are antiparallel. The minimum magnitude of the resultant is zero.