My Math Forum Help with vector based issue

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 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 0-1) 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 0-1 with this vector sum Think of defining it with normalizing it to 0-1 https://en.wikipedia.org/wiki/Norm_(mathematics) use 1-norm 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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