What is the Maximum Magnitude of a Vector Sum?

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The maximum magnitude of the vector sum of a vector with magnitude 20 and another with magnitude 25 is 45, achieved when the vectors are aligned in the same direction. The minimum magnitude is 5, occurring when the vectors are opposite to each other. The discussion highlights the importance of vector direction in determining the resultant magnitude. Participants expressed confusion about how to calculate the sum without knowing the angle between the vectors. The conversation clarified the rules governing vector addition, leading to a better understanding of the problem.
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Homework Statement



A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be:
A. Zero
B. 3
C. 12
D. 47
E. 50

Homework Equations



Probable the Pythagoreans and use of sin, cos, etc.

The Attempt at a Solution



Not sure how to add the magnitude of vector w/out knowing the angle or the different components.
Thanks for looking at the problem.
 
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vorse said:

Homework Statement



A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be:
A. Zero
B. 3
C. 12
D. 47
E. 50

Homework Equations



Probable the Pythagoreans and use of sin, cos, etc.

The Attempt at a Solution



Not sure how to add the magnitude of vector w/out knowing the angle or the different components.

Thanks for looking at the problem.

Welcome to PF.

Maybe eliminate the answers that aren't possible?
 
I know what the answer it. I just don't know how the answer key got there. There are some rules that constrain the addition/subtraction of magnitude of vectors, but I don't know what they are. I am searching the net but to no avail.P.S
Thanks for the welcome.
 
vorse said:
I know what the answer it. I just don't know how the answer key got there. There are some rules that constrain the addition/subtraction of magnitude of vectors, but I don't know what they are. I am searching the net but to no avail.


P.S
Thanks for the welcome.


If you have those two force acting on a body, when would the resultant force be maximum and when would they be minimum?
 
vorse said:
I know what the answer it. I just don't know how the answer key got there. There are some rules that constrain the addition/subtraction of magnitude of vectors, but I don't know what they are. I am searching the net but to no avail.

P.S
Thanks for the welcome.

You know that depending on direction a vector can be added head to tail right? So the biggest value the result can be is ... |20| + |25|

Likewise the smallest value the result can be is when they are in opposite directions. |25| - |20|

Looks like there is only one answer that satisfies these conditions.
 
LowlyPion said:
You know that depending on direction a vector can be added head to tail right? So the biggest value the result can be is ... |20| + |25|

Likewise the smallest value the result can be is when they are in opposite directions. |25| - |20|

Looks like there is only one answer that satisfies these conditions.


Yea, this was the rule I was looking for. Thanks a lot Pion.
 

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