June 19th, 2016, 11:52 AM  #1 
Newbie Joined: Jun 2016 From: UK Posts: 3 Thanks: 0  Help with vector based issue
Hello all! Firstly, I apologize for my lack of knowledge in this field, I'm struggling with what I'm sure is a simple issue, but it's beyond me right now. Ok so.. I'm trying to figure out the "weight" of a set of vectors that are added together to form a "final" vector. For example: vector1 = (5,5) vector2 = (6,5) vector3 = (3,5) finalVector = vector1 + vector2 + vector3 How would I workout the "weight" (normalized 01) that vector2 has on the finalVector position? Thank you for any help you can give. Mike. 
June 19th, 2016, 01:53 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,704 Thanks: 669 
"weight" is undefined in this context. It could mean length or length squared.

June 21st, 2016, 01:31 PM  #3 
Newbie Joined: Jun 2016 From: UK Posts: 3 Thanks: 0 
Thank you for the reply mathman. Ah ok, I understand. If finalVector is the full movement of a 2d point from (0,0) to finalVector. Is there a way to find out "how much" or the "percentage" of the finalVector movement that each vector contributes? 
June 21st, 2016, 04:52 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,704 Thanks: 669 
You still need a precise definition of weight.

June 22nd, 2016, 04:12 AM  #5 
Newbie Joined: Jun 2016 From: Hong Kong Posts: 20 Thanks: 2 
$\displaystyle v_1=(5,5),v_2=(6,5),v_3=(3,5)$ The normal defined vector sum is $\displaystyle v_1+v_2+v_3=(2,15)$ This kind of sum may cause data lose of "weight" by some means You can't normalize it to 01 with this vector sum Think of defining it with normalizing it to 01 https://en.wikipedia.org/wiki/Norm_(mathematics) use 1norm to define "weight" for each vector $\displaystyle v_1_1=10,v_2_1=11,v_3_1=8$ $\displaystyle v_1_1+v_2_1+v_3_1=29$ $\displaystyle weight(v_1)=\frac{10}{29},weight(v_2)=\frac{11}{29 },weight(v_3)=\frac{8}{29}$ Generally,$\displaystyle weight(v_i,p)=\frac{v_i_p}{\sum_i v_i_p}$ 
June 22nd, 2016, 12:43 PM  #6 
Newbie Joined: Jun 2016 From: UK Posts: 3 Thanks: 0 
Thank you for the replies, mathman, fungarwai. fungarwai! Thank you so much for the detailed reply. This is a big, big help in solving my problem. It's almost there, the only issue I have is a slight data loss in "weight" that I'm getting from this method, that you mentioned. Is there any way around this? Any topics I can study to guide me in the right direction to something that will help? Thanks again. 
June 23rd, 2016, 03:42 AM  #7 
Newbie Joined: Jun 2016 From: Hong Kong Posts: 20 Thanks: 2 
I learn these from lessons about matrix May called linear algebra, functional analysis as wikipedia mentioned 

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