Proving the Dot Product and Norm Theorems

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Homework Help Overview

The discussion revolves around proving the dot product and norm theorems, specifically focusing on the relationship between vectors and their properties in a geometric context.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to manipulate an equation involving vectors but expresses uncertainty about the implications of the right side. Other participants engage by discussing the conditions under which the dot product is zero and the geometric interpretation of the vectors involved.

Discussion Status

The conversation is ongoing, with participants exploring different interpretations of the relationships between the vectors. Some guidance has been offered regarding the conditions for perpendicularity, but no consensus has been reached on the original poster's approach.

Contextual Notes

There appears to be some ambiguity regarding the definitions and relationships of the vectors involved, particularly in relation to their geometric representation as radii of a circle.

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Homework Statement


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The Attempt at a Solution


I let D be the center x = DX & a = DA

(x-a) * (x+a)=|x|^2-|a|^2

Dunno what to do with the right side of the equation
 
Last edited:
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The right side is zero, since x = a, and if a dot product of two vectors is zero they are perpendicular.
 
x = a since both the radius of the circle correct?
 
Yes.
 

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