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Proving a given vector equation

  • Thread starter MarcL
  • Start date
  • #1
170
2

Homework Statement


Prove ||u+v||^2 + ||u-v||^2=2||u||^2+2||v||^2

Homework Equations


* This is the part I can't figure out*

The Attempt at a Solution


anybody got an idea where I can start? I can't seem to remember the property I can use to simplify ||u+v||^2

P.S sorry for the vague title, i really didn't know what to put in there.
 
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Answers and Replies

  • #2
11,501
5,052
Are u and v vectors?
 
  • #3
170
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Yes! sorry I should have italized them , copy pasted it, Ill edit it right now
 
  • #4
11,501
5,052
What can you say about u+v and u-v?
 
  • #5
170
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Hmmmm, Not too sure what I can say, but geometrically they are two sides of a parallelogram, and u+v / u-v is the line across it
 
  • #6
11,501
5,052
Have you tried using the vector dot product for u+v and for u-v?

Hint replace the (u+v)^2 with its dot product
 
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  • #7
170
2
Ahhh I see so I do u+v dot u+v ? then just distribute and use the idea that u dot u = ||u||?
 
  • #8
11,501
5,052
I think you have it now. I hope my hint wasn't too obvious.
 
  • #9
170
2
nope lead me in the right direction. Thank you so much!
 
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