Concept explainers
If
To Determine:
Whether the magnitude of the sum of two vectors is necessarily greater than the magnitude of V1 and/or V2.
Solution:
No, the magnitude of the sum of two vectors is not necessarily greater than the magnitude of
Explanation:
The sum of the vector could result in a shorter vector than the original ones, therefore the magnitude would be less than the other vectors. The resultant magnitude depends on the direction in which the two vectors are inclined.
The resultant magnitude of vector can be obtained by:
Here, the maximum value of
If
This implies that the value of V is greater than the value of each
This implies that the value of V is less than the value of each
Conclusions:
The magnitude of the sum of the vectors could be greater than the magnitude of any of the vectors, but not always.
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Physics: Principles with Applications
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