When adding two vectors, their resultant vector’s magnitude can be calculated using the triangle inequality theorem. For two vectors, A and B, the possible range of magnitudes for the resultant vector R can be defined as:
- |A| – |B| < |R| < |A| + |B|.
In this specific case, we have a vector A with a magnitude of 3 and another vector B with a magnitude of 4. Using the triangular inequality:
- The minimum possible magnitude for the resultant vector R is: |R|min = |3| – |4| = 3 – 4 = -1 (which we discard as magnitude cannot be negative).
- The maximum possible magnitude for R is: |R|max = |3| + |4| = 3 + 4 = 7.
Therefore, the possible range of magnitudes for the resultant vector R is:
- 0 < |R| < 7.
From this analysis, it can be concluded:
- The resultant vector magnitude cannot be less than 0 or more than 7. Specifically, the following magnitudes are impossible for the resultant vector:
- |R| = 0, because this would imply that the vectors cancel each other out completely, which is not possible given their magnitudes.
- Any magnitude greater than |R| = 7 is also impossible.
In summary, the magnitudes that are not possible when adding a vector of magnitude 3 to a vector of magnitude 4 are:
- 0
- Any value greater than 7
.