Dot product between cross products

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Homework Help Overview

The discussion revolves around proving the equation involving the dot product of two cross products, specifically (a x b) · (c x d) = |a·c b·c| |a·d b·d|. Participants express confusion regarding the notation and the right-hand side of the equation.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to understand the notation used in the equation and questions whether the symbols represent modulus lines or matrix brackets. They express uncertainty about how to start the proof without clarity on the right-hand side. Other participants suggest using the Levi-Civita symbol as a method to approach the cross products, while one participant notes they have completed the proof without that symbol.

Discussion Status

The discussion is ongoing, with participants sharing different perspectives on how to approach the proof. Some guidance has been offered regarding the use of the Levi-Civita symbol, but there is no explicit consensus on the best method to proceed.

Contextual Notes

There is uncertainty regarding the notation used in the equation, and participants are exploring different interpretations of the right-hand side. The original poster's lack of understanding of the notation may be a constraint in their ability to engage with the problem effectively.

quietrain
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Homework Statement


show (axb) . (cxd) =
|a.c b.c|
|a.d b.d|

The Attempt at a Solution



i have no idea. i don't know if the lines at the side are modulus lines or matrix brackets

but it seems that it has something to do with distribution law.

but i can't start proving if i don't even understand what the right hand side of the equation is ><

thanks for help!
 
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Right side is a determinant of this matrix. It's not so hard to prove, you could in example use Levi-Civita symbol to write your cross product, it goes in 3 steps afterwards.
 
irycio said:
Right side is a determinant of this matrix. It's not so hard to prove, you could in example use Levi-Civita symbol to write your cross product, it goes in 3 steps afterwards.

oh i have done it. but i didn't use that symbol? thanks anyway!
 
Well, you don't have to use it, that's just my favourite way to deal with cross product stuff :).
 

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