Results 1 to 7 of 7

Math Help - Vectors: orthogonal / opposite

  1. #1
    Banned
    Joined
    Apr 2009
    Posts
    27

    Vectors: orthogonal / opposite

    x=<3, 2, -4>
    y=<-3/2, 1, -2>
    z=<0, 2, 1>

    Which of these statements apply?

    1. vectors x and y are orthogonal
    2. vectors x and y are in opposite directions
    3. vectors x amd z are orthogonal
    4. vectors x and z are in opposite directions
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2009
    Posts
    15
    If two vectors are orthogonal (ie. perpendicular to each other), then their dot product will be zero, because the angle between them is 90 degrees. You could use this to either rule out two of them or find your answer.

    dot product:
    <a,b,c> . <d,e,f> = (a x d) + (b x e) + (c x f)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Apr 2009
    Posts
    27
    It seems like c is the only statement that applies since the dot product of a and z equals 0. I don't think any of the vectors are opposites of another since there does not exist a negative scalar that would make one vector equal another. Is this the correct way to compute opposites?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Gamma's Avatar
    Joined
    Dec 2008
    From
    Iowa City, IA
    Posts
    517

    Dot Product

    |\vec{v_1}||\vec{v_2}|cos(\theta)=v_1\cdot v_2

    This might be of some use as you can solve for \theta which is the angle between the vectors.

    \theta=arccos\left(\frac{v_1\cdot v_2}{|\vec{v_1}||\vec{v_2}|}\right)
    Last edited by Gamma; April 22nd 2009 at 04:50 PM. Reason: LaTeX error
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2009
    Posts
    15
    I'd say two vectors are opposite if they're parallel but their directions are opposite. ie. (x,y,z) and (-ax,-ay,-az), where a is any positive real number and x, y and z are any real numbers, positive or negative. That's what you had in mind, yeah? So with that definition, I'd say you're correct thinking that c is the only true statement
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    May 2009
    Posts
    1

    Test Question

    This is a test question and my student had no business posting it here!
    Dr. B
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Oct 2005
    From
    Earth
    Posts
    1,599
    Quote Originally Posted by amburden View Post
    This is a test question and my student had no business posting it here!
    Dr. B
    Thread closed while this is reviewed.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Orthogonal vectors
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: May 17th 2011, 12:27 PM
  2. [SOLVED] Orthogonal vectors
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: April 24th 2011, 01:16 AM
  3. Orthogonal Vectors
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 9th 2010, 05:05 PM
  4. vectors orthogonal etc.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 2nd 2009, 07:35 PM
  5. orthogonal vectors
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 19th 2009, 12:20 PM

Search Tags


/mathhelpforum @mathhelpforum