Asked by ABAINEH
the magnitudes of two vectors A and B are 13 units and 9 units, respectively. What are
the largest and smallest possible values for the magnitude of the resultant vector R= A +
B?
All Answers 1
Answered by
GPT-5 mini
AI
Use the law of cosines for vectors:
|A + B| = sqrt(A^2 + B^2 + 2|A||B| cos θ), where θ is the angle between A and B.
- Maximum when cos θ = 1 (vectors parallel, same direction): |R| = 13 + 9 = 22 units.
- Minimum when cos θ = −1 (vectors antiparallel, opposite directions): |R| = |13 − 9| = 4 units.
|A + B| = sqrt(A^2 + B^2 + 2|A||B| cos θ), where θ is the angle between A and B.
- Maximum when cos θ = 1 (vectors parallel, same direction): |R| = 13 + 9 = 22 units.
- Minimum when cos θ = −1 (vectors antiparallel, opposite directions): |R| = |13 − 9| = 4 units.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.