1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Orthonormal Basis of a Plane

  1. May 24, 2006 #1
    I need to find the Orthonormal Basis of this plane:

    x - 4y -z = 0

    I know the result will be the span of two vectors but I'm not sure where to start. Any hints?


  2. jcsd
  3. May 24, 2006 #2


    User Avatar
    Science Advisor
    Homework Helper

    First find a basis by finding two independent vectors that satisfy that equation. This is easy: find one non-zero vector satisfying that equation with z-component 0, and find another satisfying that equaiton with y-componenet 0. Next, orthogonalize this basis using Gramm-Schmidt. Finally, normalize it by dividing the two orthogonal vectors you have by their own norms.
  4. May 24, 2006 #3
    So set (y=1, z=0) and (y=0, z=1)

    Get two vectors:

    (4,1,0) and (1,0,1)


    (4/sqrt(17), 1/sqrt(17), 0) and (1/sqrt(2), 0, 1/sqrt(2))
  5. May 24, 2006 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    To satisfy the "ortho" part of Orthonormal you need to verify that the dot product of your 2 vectors is 0.
  6. May 24, 2006 #5
    Ah thanks,

    so e1= (1/sqrt(2), 0, 1/sqrt(2))

    e2 = (2/3, 1/3, -2/3)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook