Concept explainers
Can the magnitude of a vector ever (a) equal, or (b) be less than, one of its components?
To Determine:
Whether the magnitude of a vector can be equal or less than one of its components.
Solution:
The magnitude may be equal but not less than one of its components.
Explanation:
For a vector’s magnitude to be equal to one of its components, that component should be equal to the magnitude and the others equal to zero. On the other hand, the magnitude of a vector will never be less than one of its components.
We need to know how to calculate the magnitude of a vector. If we define
Its magnitude is:
Let suppose:
Then:
Even if the value of the component is negative, for finding the resultant, it will be squared and hence, the resultant would be greater than 0 the value of resultant cannot be reduced below the value of the component.
Conclusions:
The vector magnitude is always greater or equal to one of its components but never less than one of them.
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