Results 1 to 7 of 7

Math Help - Deduce Triangle Equality! [Vectors]

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    31

    Deduce Triangle Equality! [Vectors]

    Alright people im struggling with this vector question;

    Deduce the triangle inequality,
    ||a-c|| <= ||a-b|| + ||b-c||

    Ive been stuck on this question for ages now, and ive tried various attempts to solving it.

    Can any one help me out? Cheers
    David.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    Did you think about using vectors ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2009
    Posts
    31
    Quote Originally Posted by Bacterius View Post
    Did you think about using vectors ?
    You mean give an example and show it holds?
    I dont think thats valid as you have to deduce it?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    No, I meant using vector properties (they go quite well with triangles) and look if you can't work out your equality from this. By the way, is your triangle scalene or is it some particular type of triangle ? And what do you mean by ||a-c|| ? Does it mean the length of the vector \vec{AC}, which is ||\vec{AC}|| ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Oct 2009
    Posts
    31
    Quote Originally Posted by Bacterius View Post
    No, I meant using vector properties (they go quite well with triangles) and look if you can't work out your equality from this. By the way, is your triangle scalene or is it some particular type of triangle ? And what do you mean by ||a-c|| ? Does it mean the length of the vector \vec{AC}, which is ||\vec{AC}|| ?
    Yeah i tryed using vector properties and yeah || a || means the length of the vector a e.g. (a1^2 + a2^2 + ... + an^2)^1/2

    I still couldent work it out, using properties like;

    || a - b ||^2 = ||a||^2 ||b||^2 -2cos x.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    Quote Originally Posted by simpleas123 View Post
    Yeah i tryed using vector properties and yeah || a || means the length of the vector a e.g. (a1^2 + a2^2 + ... + an^2)^1/2

    I still couldent work it out, using properties like;

    || a - b ||^2 = ||a||^2 ||b||^2 -2cos x.
    ||a-c|| <= ||a-b|| + ||b-c||

    Does it mean :

    ||\vec{AC}|| <= ||\vec{AB}|| + ||\vec{BC}|| ?

    One really needs to know what you mean to be able to help you.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Oct 2009
    Posts
    31
    Quote Originally Posted by Bacterius View Post
    ||a-c|| <= ||a-b|| + ||b-c||

    Does it mean :

    ||\vec{AC}|| <= ||\vec{AB}|| + ||\vec{BC}|| ?

    One really needs to know what you mean to be able to help you.
    Yes it does, sorry for the fusion.

    I know that ||\vec{AC}|| = ||\vec{AB}|| + ||\vec{BC}||
    If and only if the dot product of two of the vectors = 0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: December 17th 2011, 12:48 PM
  2. Triangle. Equality of angles
    Posted in the Geometry Forum
    Replies: 4
    Last Post: October 27th 2010, 08:59 AM
  3. vectors: right triangle
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 24th 2010, 01:19 PM
  4. Vectors/Triangle Help Please
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 4th 2009, 05:15 AM
  5. area of triangle using 3d vectors
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 25th 2009, 04:35 PM

Search Tags


/mathhelpforum @mathhelpforum