A vector of magnitude 20 is added to a vector of magnitude 25.

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When adding a vector of magnitude 20 to a vector of magnitude 25, the resultant vector's magnitude can vary based on their directions. The maximum possible magnitude occurs when both vectors are aligned, resulting in 45, while the minimum occurs when they are directly opposing, yielding 5. Given the choices of 50, 47, 3, 0, and 12, only 12 falls within the possible range of resultant magnitudes. Therefore, 12 is identified as the correct answer. More information about the vectors' directions is necessary for precise calculations.
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Homework Statement



A vector of magnitude 20 is added to a vector of magnitude 25. What could the magnitude of the sum be?

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The Attempt at a Solution



I am given a list of choices. But, it seems to me like it could be just about anything, because I have no idea what the direction of both vectors are. Can anyone give me a place to start?
 
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Well, the best I can say is that there does exist a minimum magnitude the resultant vector could be and a maximum. Unless all but 1 answer is outside of this range, you would need more information.
 
True. If I assume they are in the exact same direction, I can have 45, which is the max. If I assume they are directly opposing, I get 5 as a minimum.

My choices are 50, 47, 3, 0, and 12. So it would seem 12 is correct?
 
Yes, that is the only value that could possibly be attained by adding vectors with those magnitudes.
 

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