Is the Vector Product Really a Vector?

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Homework Help Overview

The discussion revolves around the nature of the vector (cross or external) product and whether it can be classified as a vector. The original poster seeks to understand the physical and mathematical justification for this classification within the context of a math physics course.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants suggest that the definition of the cross product inherently implies it is a vector. Others raise questions about the criteria used to define a vector, including transformation rules and properties that the cross product must satisfy.

Discussion Status

The discussion is exploring various interpretations of what constitutes a vector, with participants questioning the definitions and properties involved. There is no explicit consensus yet, but the dialogue appears to be productive in examining the underlying assumptions.

Contextual Notes

Participants are considering the definitions and properties of vectors in relation to the cross product, which may involve specific mathematical frameworks or physical interpretations that are not fully detailed in the posts.

golshah
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Homework Statement

How can I prove that the vector (cross or external) product is really and physically a vector. I face with this problem in math physics course.
thanks for your hint.


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The Attempt at a Solution

 
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I think the fact that the crossproduct is a vector follows immediately from the definition of the cross product.
 
you find torque with the cross product you need two vectors in order to find it and the resulting torque is normal to the other 2
 
What are you using as a definition of a vector? For example, does a vector obey a certain transformation rule? Does the cross product satisfy the required properties.
 

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