Why doesn't 2A+2B=2C work for three equal vectors?

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rasen58
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Homework Statement


The diagram shows 3 vector all of equal length. Which statement is true?
a. A+B=A-C
b. A+B=B-C
c. A-B=2A-C
d. A-B=2A+C
e. 2A+2B=2C
Diagram of three equal-length vectors forming a closed triangle: arrows labelled A (along the bottom, pointing right), B (up the right side, pointing toward the top vertex) and C (down the left side, pointing toward the bottom-left vertex).


Homework Equations


None

The Attempt at a Solution


I just added them in my head, and thought that e. 2A+2B=2C would also work. Why doesn't it?
 
Attachments
  • Diagram of three equal-length vectors forming a triangle: A along the bottom pointing right, B up and to the right, and C down and to the left, each labeled with an arrowhead.
    upload_2015-1-3_18-52-4.png
    11.9 KB · Views: 541
  • Triangle of three equal-length vectors labelled A, B and C, arranged head to tail: A points right along the base, B points up-left from the bottom-right corner to the apex, and C points down-left from the apex to the bottom-left corner.
    upload_2015-1-3_18-52-4.png
    44.7 KB · Views: 569

Discussion

To see where you might have gone wrong, try the following. On a sheet of paper, draw just the two sides of the triangle representing A and B making sure you include the arrow heads. Now, on that picture, draw in the vector that represents the result of adding A and B making sure you include the arrow head on the result. Now compare your resultant vector with the vector C in the original picture.
 
The resultant points in the direction that C is pointing in the image.
 
rasen58 said:
The resultant points in the direction that C is pointing in the image.
Not correct.
 
rasen58 said:
The resultant points in the direction that C is pointing in the image.

No, this is the reason you're having trouble with the problem. See the attached figure and try to answer the question shown there. If you need to, refer back to the link I gave earlier or check your notes or textbook.
 
Attachments
  • Triangle of vectors with A drawn as a horizontal arrow along the bottom pointing right, and B drawn as the right-hand side pointing up-left to the apex. A handwritten-style note asks on which end of the left side the arrow head should go to represent A + B.
    Vector Addition.png
    4.2 KB · Views: 548
Oh I see, C should be pointing from the tail of A to the head of B.
But then the magnitude of C would still be the same though, so how does that help?
 
rasen58 said:
Oh I see, C should be pointing from the tail of A to the head of B.
But then the magnitude of C would still be the same though, so how does that help?
Those equations in the Original Post are vector equations.

It's not that C should be in the opposite direction, it's that the resultant of adding A and B is -C .
 
rasen58 said:
C should be pointing from the tail of A to the head of B.
The resultant of A and B points that way. Saying C points that way when C is already defined the other way in the problem statement is confusing.
rasen58 said:
the magnitude of C would still be the same though,
Yes, but the question doesn't ask about magnitudes.
 
SammyS said:
It's not that C should be in the opposite direction, it's that the resultant of adding A and B is -C .
Oh wow, I see now. Thanks.
 

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