Vector Multiplication: a-b X a+b = 2(aXb)

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Discussion Overview

The discussion revolves around the vector multiplication identity (a-b) X (a+b) = 2(a X b), focusing on the properties of the cross product and methods for expanding and simplifying the expression. The scope includes mathematical reasoning and technical explanation related to vector operations.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant presents the identity (a-b) X (a+b) = 2(a X b) as a statement to be explored.
  • Another participant asks about the methods attempted to solve or verify the identity, suggesting starting with the definition of cross multiplication.
  • A different participant shares their experience of expanding the vectors using specific components, indicating that the left side becomes complex.
  • One participant suggests directly multiplying the given expression, noting that there are four cross products to consider, with two resulting in zero.
  • Another participant emphasizes the distributive property of the cross product and suggests using it along with other properties to simplify the problem without resorting to component-wise calculations.

Areas of Agreement / Disagreement

Participants express differing approaches to the problem, with no consensus on the best method to simplify or verify the identity. The discussion remains unresolved regarding the most effective strategy.

Contextual Notes

Some participants highlight the complexity of the expression when expanded, and there are references to the properties of the cross product that may influence the outcome. Specific assumptions about vector components and operations are not fully detailed.

physicsss
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(a-b)X(a+b)=2(aXb), where a and b are vectors.

Thank you.
 
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What have you tried so far?

I would start with the definition of cross multiplication.
 
I tried to set a=<x,y,z> and b=<x1,y1,z1> and expand everything...and the left side became a big mess.
 
Why don't u multiply exactly what u were given...?I mean there are exactly 4 cross products u'd be getting,when doing it.2 of them are 0...

Daniel.
 
The cross product is distributive. Use that and some of its other properties to get the answer. No need to fiddle with components.
 

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