Results 1 to 4 of 4

Math Help - Sum of 3 vectors in R3

  1. #1
    Junior Member
    Joined
    Feb 2013
    From
    Charlotte, NC
    Posts
    50

    Sum of 3 vectors in R3

    If the sum of three vectors in R3 is zero, must they lie in the same plane?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,668
    Thanks
    609

    Re: Sum of 3 vectors in R3

    Hey Civy71.

    They could lie all on the same line or the same plane. They all lie on the same point if all vectors are the zero vector.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member MacstersUndead's Avatar
    Joined
    Jan 2009
    Posts
    291
    Thanks
    32

    Re: Sum of 3 vectors in R3

    Let the three vectors be v_1,v_2,v_3

    If the sum of the three vectors is the zero vector, then these vectors are linearly dependent since v_3 = -v_1 -v_2 so v_3 must lie on the same plane spanned by v_1 and v_2. Hence all three vectors lie on the same plane
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Feb 2013
    From
    Charlotte, NC
    Posts
    50

    Re: Sum of 3 vectors in R3

    Thanks for the help MacstersUndead. Cool Avatar picture.
    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: 3
    Last Post: June 30th 2011, 08:05 PM
  3. Replies: 2
    Last Post: June 18th 2011, 10:31 AM
  4. [SOLVED] Vectors: Finding coefficients to scalars with given vectors.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 23rd 2011, 12:47 AM
  5. Replies: 4
    Last Post: May 10th 2009, 06:03 PM

Search Tags


/mathhelpforum @mathhelpforum