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July 21st, 2017, 09:49 AM  #1 
Newbie Joined: Jun 2017 From: Earth Posts: 16 Thanks: 0  Does anyone know what this theorem and its proof is talking about?
This is the theorem and its proof: I totally have no idea what the author was trying to convey. The vector sum $\displaystyle \bar{AB}+\bar{BC}+\bar{CA}$ is certainly always equal to zero, no matter the three points A, B and C are collinear or not. So how should I understand this theorem and its proof? Thanks a lot for your help. PS: maybe the concept of "statical addition" is the key, the following is the definition of it in the book, just for your reference, but I can get no clue from the definition that can help me with the theorem. 
July 23rd, 2017, 04:49 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,582 Thanks: 668 
It looks to me like the problem is not so much the definition of "static addition" as it is the definition of "line vector". What is that definition? The only references to "line vectors" I could find on the internet are references to computer graphics.

July 23rd, 2017, 06:11 AM  #3  
Newbie Joined: Jun 2017 From: Earth Posts: 16 Thanks: 0  Quote:
 
July 23rd, 2017, 06:15 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,611 Thanks: 1297 
I would imagine this theorem applies to vectors restricted to a single dimension.

July 23rd, 2017, 07:07 AM  #5 
Senior Member Joined: Jun 2015 From: England Posts: 644 Thanks: 184 
Where does it say that A, B and C are in the same plane? Three points A, B, C have position vectors a, b and c respectively. A, B and C are collinear if and only if (a x b) + (b x c) + (c x a) = 0 using the cross products. 
July 23rd, 2017, 08:05 PM  #6 
Newbie Joined: Jun 2017 From: Earth Posts: 16 Thanks: 0  I know it, but does it have anything to do with my original question? Also, I can't catch your first question; I don't understand why you ask that.


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