Results 1 to 3 of 3

Math Help - vectors scalar product help

  1. #1
    Super Member
    Joined
    Sep 2008
    Posts
    607

    vectors scalar product help

    Use properties of the scalar product to prove that for all vectors u,v  \in  R^{2}

     \lvert u+v \rvert^{2} + \lvert u-v \rvert^{2} = 2\lvert u \rvert^{2} + 2\lvert v \rvert^{2}

    i have expanded this got the above results, however I dont see how to use properties of the scalar product, i have simply applied some basic algebra?
    Last edited by Tweety; November 15th 2012 at 12:21 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: vectors scalar product help

    Quote Originally Posted by Tweety View Post
    Use properties of the scalar product to prove that for all vectors u,v  \in  R^{2}
     \lvert u+v \rvert^{2} + \lvert u-v \rvert^{2} = 2\lvert u \rvert^{2} + 2\lvert v \rvert^{2}
    i have expanded this got the above results
    I have no idea what that could mean!

    \|u\pm v\|^2=(u\pm v)\cdot(u\pm v)=u\cdot u\pm 2 u\cdot v+v\cdot v
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,368
    Thanks
    1313

    Re: vectors scalar product help

    Stricty speaking |u- v|^2 is the scalar product of the vector u- v with itself- that's one property of "scalar product". |u- v|^2= (u- v)\cdot(u- v)= u\cdot u- u\cdot v- v\cdot u+ v\cdot v. Another property of the scalar product is that it is commutative- u\cdot v= v\cdot u so that -u\cdot v- v\cdot u= -u\cdot v- u\cdot v= -2u\cdot v.

    Do the same with |u+ v|^2.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: December 17th 2010, 08:19 AM
  2. Replies: 6
    Last Post: September 7th 2010, 09:03 PM
  3. multivariable differential for inner product(scalar product)?
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 23rd 2009, 05:40 PM
  4. Scalar product of vectors question
    Posted in the Geometry Forum
    Replies: 4
    Last Post: October 13th 2009, 04:18 AM
  5. scalar triple product, coplanar vectors.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 24th 2009, 10:24 AM

Search Tags


/mathhelpforum @mathhelpforum