Algebraic Question: e(e*a) - e x (e x a) = 3a?

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Homework Help Overview

The discussion revolves around an algebraic expression involving unit vectors and operations such as dot products and cross products. The original poster is attempting to simplify the expression e(e*a) - e x (e x a) and is questioning their algebraic manipulation, as they consistently arrive at 3a instead of a.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster describes their approach to the problem, including matrix operations and the use of vector identities. They express uncertainty about their results and seek clarification on their algebraic steps.

Discussion Status

Participants are engaging with the original poster's work, with one member requesting to see the detailed steps of their calculations. Another participant suggests using vector identities to approach the problem, indicating a potential shift in method without reaching a consensus on the solution.

Contextual Notes

The original poster expresses confusion about the placement of their question, suggesting they may be uncertain about the forum's guidelines or the appropriateness of their post in the current context.

KleZMeR
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ok, this is my first post here so i don't know what kind of questions i can ask, so i'll fire away...
e is unit vector, I'm showing a = e(e*a) - e x (e x a), where * is the dot-product and x is the cross product, i keep getting 3a, not a. Is my algebra off or?...
 
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Can you show your work so we can see where you might be going wrong?
 
well that's a lot of stuff, ok i'll try, these are simple matrix operations, i think my positive/negative alternating on row operations are ok when finding det a, but still, the rhs is where the problem must be because e(e*a)=a, right?? so

a= c1x + c2y + c3z

and taking both cross products, e x (e x a), because all scalars of e = 1 i get

c1 + c2 + c3 - ((c2-c1) - (c1-c3))x = 3c1
c1 + c2 + c3 - ((c3-c2) - (c2-c1))y = 3c2
c1 + c2 + c3 - ((c1-c3) - (c3-c2))z = 3c3

so is this not =3a ??

why was this question moved? did i post it in the wrong place?
 
Use vector identities instead.

a x (b x c) = (a.c)b - (a.b)c
 
thanks
 

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