1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Transitive Property with Orthogonal Vectors?

  1. Apr 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Let x1, x2, and x3 be vectors in R^3. If x1 is orthogonal to x2 and x2 is orthogonal to x3, is it necessarily true that x1 is orthogonal to x3?


    2. Relevant equations

    I know that if x1 is orthogonal to x2 and x2 is orthogonal to x3, then...

    (x1)^T*x2=0
    (x2)^T*x3=0


    3. The attempt at a solution

    I think that the answer would be no. I can imagine it geometrically, but I'm not sure how I would prove this algebraically.

    I would obviously have to prove that (x1)^T*x3 would ALWAYS have to equal 0 if it the statement was necessarily true... but I'm not sure how to go about doing that...

    I'm completely stuck. I would greatly appreciate your help!
     
  2. jcsd
  3. Apr 20, 2010 #2

    radou

    User Avatar
    Homework Helper

    Try to think of an example.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Transitive Property with Orthogonal Vectors?
  1. Orthogonal vectors (Replies: 14)

  2. Orthogonal vectors (Replies: 7)

  3. Orthogonal vectors (Replies: 29)

Loading...