Proving Parallel Vectors: |u•v| = ||u|| ||v||

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Homework Help Overview

The original poster attempts to demonstrate that the absolute value of the dot product of two vectors, |u•v|, equals the product of their magnitudes, ||u|| ||v||, under the condition that the vectors u and v are parallel. There appears to be some confusion regarding the definition of the dot product and its implications for parallel vectors.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question the original poster's understanding of the dot product, particularly the assertion that parallel vectors have a dot product of 1. There is a discussion about the proper definition of the dot product and its relationship to vector multiplication.

Discussion Status

The discussion is ongoing, with participants seeking clarification on definitions and exploring the implications of different types of vector multiplication. Some guidance has been offered regarding the need for a clearer understanding of the dot product.

Contextual Notes

There is an indication that the original poster may have misunderstood the relationship between the dot product and parallel vectors, as well as the definitions involved in vector operations. The conversation reflects a need for precise definitions in the context of the problem.

dangish
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Question: Show that |u dot v| = ||u|| ||v|| if and only if u and v are parallel.

I know that u and v are parellel if their dot product is 1.

so if |u dot v| = 1 , fair enough, but how can I show that ||u|| ||v|| will also be equal to 1

any help would be greatly appreciated, thanks in advance :)
 
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Do you know the definition of the dot product?
 
dangish said:
I know that u and v are parellel if their dot product is 1.

This is not true. You must have misunderstood something...

How did you define the dot product?
 
Not really.. it's just the product of two vectors isn't it?
 
No, check out the proper definition and then look at your problem again, it should become very clear :wink:
 
Could you perhaps tell me your definition of the dot product? :D
 
dangish said:
Not really.. it's just the product of two vectors isn't it?
This is so vague as to be meaningless.

dangish said:
Could you perhaps tell me your definition of the dot product? :D
You tell us, please.
 
Mark44 said:
This is so vague as to be meaningless.

sorry champ
 
  • #10
My point is that since there are several ways that vectors can be multiplied, you need to be more specific.

u \cdot v - the dot product, sometimes called the scalar product because it results in a scalare
u X v - the cross product for vectors in R3
av - scalar multiplication of a scalar and a vector
 

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