Dot product (scalar product) of 2 vectors: ABcos[itex]\theta[/itex]

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Discussion Overview

The discussion revolves around the derivation and understanding of the dot product (scalar product) of two vectors, specifically the term Bcosθ in the expression A·B = ABcosθ. Participants explore the conceptual basis and mathematical interpretation of this relationship.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses confusion about how the term Bcosθ is derived, questioning the simplicity of the relationship and the role of the vector A.
  • Another participant shares a link to a Wikipedia article that provides a proof of the geometric interpretation of the dot product, suggesting it may clarify the confusion.
  • A later reply acknowledges the complexity of the information and indicates a need for further self-study to better understand the concept, with hopes of returning with more specific questions.
  • One participant concludes that they have figured out the concept, but mentions having another unrelated vector question to discuss in a new thread.

Areas of Agreement / Disagreement

The discussion reflects a lack of consensus, as one participant is confused about the derivation while another finds clarity after reviewing additional resources. The initial confusion remains unresolved for some participants.

Contextual Notes

Participants express uncertainty regarding the derivation of the Bcosθ term and the role of vector A, indicating potential limitations in their understanding of the geometric interpretation of the dot product.

LearninDaMath
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How, precisely, do you get/derive the Bcosθ term?



Is it simply [Cosθ=A/B] --> [BCosθ = A] ? It can't be that simple because then how is the extra length of vector A fit into [*A*Bcosθ]? I feel pretty confused as to what is going on here. To summerize, A x B = [ABcosθ] makes little sense.. and i think that is because for one reason, I'm not sure how Bcosθ is derived. And the other reason is because I don't know where they get the A variable either. Just can't seem to see what's going on here.
 
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elfmotat said:

Wow, that looks a little more complex than I thought it would be. I thought it was something much more straight forward. I'll have to do some further self study for a little while and get back to you on what I was able to figure out. At worst, I hope to at least come back with a more specific question. At best, I'll be able to figure it out. Thanks.
 
Figured it out, this makes perfect sense now. However I have another vector question, but unrelated to this one, so I'll start a new thread for it.
 

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