Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gram-Schmidt problem - I'm stuck

  1. Dec 4, 2007 #1
    I am stuck on a problem.. I keep obtaining the incorrect answer and I am unsure of where my calculation went wrong??? I have the 2 vectors v1 [4,0,3] and v2 [25,0,-25]

    I first obtain (1/||v1||)v1 = [4/5 0 3/5] = z1

    I then proceed to do: (v2 - (z1 . v2)z1)/||v2 - (z1 . v2)|| = [25 0 -25] - 5 [4/5 0 3/5] = [25 0 -25] + [-4 0 -3] = [21 0 -28] = u2

    then 1/||u2|| = sqrt(21^2 + 0^2 + -28^2) = 35

    So i should get (1/35)[25 0 -25]

    But in the book it shows the correct answer to be:

    (1/5)[3 0 -4]?? I don't see where I went wrong.. I went over it several times.. I just must be missing something??
     
  2. jcsd
  3. Dec 4, 2007 #2
    it's so difficult to understand what you wrote but if you want to project [itex]\vec{u_1}[/itex] onto [itex]\vec{u_2}[/itex] you do this:

    [tex] \frac{\vec{u_1} \bullet \vec{u_2}}{\vec{u_1} \bullet \vec{u_1}} \vec{u_1}[/tex]

    then the orthogonal compliment is just [itex] u_1 - proj[/itex]
     
  4. Dec 5, 2007 #3
    blahh.. I don't get it.. I did and still not the right answer is produced.. can someone help.. I don't know what I am missing

    The main question is to just perform Gram-Schmidt on those first two vectors:
    4
    0
    3
    and
    25
    0
    -25

    I did it in the first post and just did it again.. I still i get a different answer then what is in the book.
     
  5. Dec 5, 2007 #4

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    I suggest taking your sweet ass time when doing the Gram-Schmidt process. It's so easy to make a mistake and one mistake just carries on.

    Do it slowly and double check and check again.
     
  6. Dec 5, 2007 #5
    I did this.. just want to make sure my formula is right for vector 2.. where u1 = what you received for the first vector.

    V2 =
    v2 - (u1 (dot product) v2)u1
    ~~~~~~~~~~~~~~~~~~~~
    ||v2 - (u1 (dot product) v2)u1||

    where ~~~~ = divide.

    I did this over and over again and seem to get (1/35)v2
     
  7. Dec 5, 2007 #6

    Galileo

    User Avatar
    Science Advisor
    Homework Helper

    EDIT: Nevermind, your first post works out doesn't it?

    You have u_2=[21 0 -28]=7[3 0 -4]

    so normalize it to get the right answer.
     
    Last edited: Dec 5, 2007
  8. Dec 5, 2007 #7
    i get how you got 7[3 0 -4]

    but for the answer it shows:

    (1/5) [3 0 -4]

    So I am still not sure how the hell they got the (1/5)
     
  9. Dec 5, 2007 #8

    Chris Hillman

    User Avatar
    Science Advisor

    What is [itex]3^2+(-4)^2[/itex]?

    Jason: in this context, is 2000 or 2007 the more memorable number? :wink:
     
  10. Dec 5, 2007 #9
    ahhhhhhhhhhhhhh alright i think i got it.. thank you all for your help.. But what happens to the 7???
     
  11. Dec 8, 2007 #10

    Galileo

    User Avatar
    Science Advisor
    Homework Helper

    You are just normalizing the vector, i.e. scale it so becomes of unit length.
    If v is a nonzero vector, then clearly v/|v| is a unit vector, where |v| is the norm of v.
    So what is the norm of 7[3 0 -4] ?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Gram-Schmidt problem - I'm stuck
  1. Gram Schmidt (Replies: 2)

  2. Gram–Schmidt process (Replies: 3)

  3. Gram-Schmidt Process (Replies: 5)

Loading...