Proving a given vector equation

MarcL · Dec 10, 2014

1. The problem statement, all variables and given/known data
Prove ||u+v||^2 + ||u-v||^2=2||u||^2+2||v||^2

2. Relevant equations
* This is the part I can't figure out*

3. 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.

jedishrfu · Dec 10, 2014

Are u and v vectors?

MarcL · Dec 10, 2014

Yes! sorry I should have italized them , copy pasted it, Ill edit it right now

jedishrfu · Dec 10, 2014

What can you say about u+v and u-v?

MarcL · Dec 10, 2014

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

jedishrfu · Dec 10, 2014

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

MarcL · Dec 10, 2014

Ahhh I see so I do u+v dot u+v ? then just distribute and use the idea that u dot u = ||u||?

jedishrfu · Dec 10, 2014

I think you have it now. I hope my hint wasn't too obvious.

MarcL · Dec 10, 2014

nope lead me in the right direction. Thank you so much!

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Proving a given vector equation

MarcL

jedishrfu

Staff: Mentor

MarcL

jedishrfu

Staff: Mentor

MarcL

jedishrfu

Staff: Mentor

MarcL

jedishrfu

Staff: Mentor

MarcL

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