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Linear algebra

  • Thread starter dangish
  • Start date
  • #1
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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 :)
 

Answers and Replies

  • #2
Do you know the definition of the dot product?
 
  • #3
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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?
 
  • #4
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Not really.. it's just the product of two vectors isn't it?
 
  • #5
No, check out the proper definition and then look at your problem again, it should become very clear :wink:
 
  • #6
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Could you perhaps tell me your definiton of the dot product? :D
 
  • #7
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Not really.. it's just the product of two vectors isn't it?
This is so vague as to be meaningless.

Could you perhaps tell me your definiton of the dot product? :D
You tell us, please.
 
  • #8
  • #9
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This is so vague as to be meaningless.
sorry champ
 
  • #10
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My point is that since there are several ways that vectors can be multiplied, you need to be more specific.

u [itex]\cdot[/itex] 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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