Results 1 to 2 of 2

Math Help - proof that 2 vectors of same length are perpindicular if subtracted

  1. #1
    Senior Member
    Joined
    Jun 2009
    Posts
    251

    proof that 2 vectors of same length are perpindicular if subtracted

    show that if u and v are any 2 vectors of the same length that u+v and u-v are perpendicular. Give a coordinate free proof using the dot product that holds true in n-space.

    So I started like this:
    |u|=|v|
    \vec u \cdot \vec v = |u|^2
    (u_1)(v_1)+(u_2)(v_2)...(u_n)(v_n) = |u|^2
    and I have no clue
    Last edited by superdude; October 26th 2009 at 03:24 PM. Reason: fixed latex
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    311
    Thanks
    2
    You need to show that (u+v).(u-v)=0
    Expand, cancel middle terms, remember that u.u = u^2 (same for v), and you've got it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 15th 2011, 05:10 PM
  2. Replies: 9
    Last Post: January 18th 2011, 01:00 AM
  3. Perpindicular vectors questions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 10th 2009, 05:45 PM
  4. how a continous can be added/subtracted with/by a discrete!?
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: July 10th 2008, 01:28 PM
  5. Replies: 3
    Last Post: March 2nd 2008, 05:00 PM

Search Tags


/mathhelpforum @mathhelpforum