Proving a given vector equation

[MarcL]

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.

 

[jedishrfu]

Are u and v vectors?

 

[MarcL]

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

 

[jedishrfu]

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

 

[MarcL]

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]

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]

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

 

[jedishrfu]

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

 

[MarcL]

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