Answer:
C) could be as small as 2.0 m, or as large as 12 m.
Explanation:
The magnitude of the vector given by the sum of the two vectors depends on the directions of the vectors.
In fact, we have two extreme conditions:
- when the two vectors have same directions, then the magnitude of their sum is equal to the sum of the magnitudes of the two vectors:
[tex]R=A+B=5.0 m + 7.0 m = 12.0 m[/tex]
- When the two vectors have opposite directions, the magnitude of their sum is equal to the difference between the magnitudes of the two vectors:
[tex]R=|A-B|=|5.0 m-7.0m|=2.0 m[/tex]
In all other intermediate cases, where the two vectors are neither parallel nor anti-parallel, the magnitude of the vector sum changes according to the components of the two vectors, and so it will span within this range of minimum length (2.0 m) and maximum length (12.0 m).
