Magnitude of the Sum of Vectors

AI Thread Summary
The discussion revolves around a physics problem involving the addition of two vectors with magnitudes of 20 and 25. The maximum possible magnitude of their sum is 45, while the minimum is 5, leading to confusion about the answer being 12. The key point is that the vectors can be at an angle to each other, affecting the resultant magnitude. By analyzing the angle between the vectors, it can be shown that a resultant magnitude of 12 is indeed possible. Understanding vector addition and the impact of angles is crucial for solving such problems.
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I'm studying for an intro Physics exam and encountered this problem on my study guide:

"A vector of magnitude 20 is added to a vector of magnitude 25.The magnitude of this sum can be:
A) 50
B) 12
C) 3
D) zero
E) none of these are possible. "

The professor told us the answer was B), but I don't understand why.

I understand that the maximum you can get with these 2 vectors is the sum (20+25=45) and that the minimum you can get is the difference (25-20=5). I don't get where the 12 is coming from though. If anyone could point me in the right direction, that would be great. Thanks!
 
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The vectors can be at an angle with respect to each other. Figure out what the angle could be based on the magnitude of the resultant vector and you will see why it's the right answer.
 

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