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October 23rd, 2015, 09:05 AM  #1 
Senior Member Joined: Oct 2014 From: Complex Field Posts: 119 Thanks: 4  Difference between projection and component
Hello, I found out that what I am calling "projection" is actually called a "component", and the difference between what I call "projection" to a real projection is that that a projection is a component multiplied by the unit vector in the direction. I wanted to know, why do we add this multipication of unit vector? I know that the regular formula of component of a vector: [A(dot)B] / (magnitude of A) is because of the triangle formed with the angle (theta) between the two vectors. so geometrically, I know what component is, but up until today I called it projection. So what is the explanation of adding the multipicationbyunitvector part? Is there a geometrical explanation? Or any other explanation? Thanks 
October 23rd, 2015, 10:02 AM  #2  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  Quote:
The "xcomponent" of a vector is, by definition, the "projection" of the vector onto the xaxis. Similarly, for the "ycomponent" and "zcomponent" relative to the projection of the vector onto the y and z axes respectively. But we can have projections onto a arbitrary line, not necessarily coordinate axes. Quote:
Quote:
 
October 24th, 2015, 06:16 PM  #3 
Senior Member Joined: Oct 2014 From: Complex Field Posts: 119 Thanks: 4 
Thank you! So tell me if I got this right: The added multipication is only if we do not project the vector on one of the coordinate axes, but if we project it on another vector. And even if we do project it on the coordinate axes, this multipication does exist, however it's not necessary because it equals to 1. Btw, you get the magnitude of the projection, right? 

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