Results 1 to 7 of 7

Math Help - planes, lines and points type of question.

  1. #1
    Junior Member
    Joined
    Feb 2006
    From
    Victoria, Australia
    Posts
    36

    planes, lines and points type of question.

    I need help with this, do i use gaussian elimination or something else.

    Three planes have eqn's given by:

    x+3y-z = 4
    2x+8y = 18
    x-y-3z = -6

    a) have no common point of intersection
    b) intersect in a point
    c) intersect in a line
    d) intersect in a plane


    cheers guys
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Glaysher's Avatar
    Joined
    Aug 2006
    From
    Newton-le-Willows
    Posts
    224
    Just noticed that you're from Australia. This isn't part of the Australian Maths Challenge is it?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2006
    From
    Victoria, Australia
    Posts
    36
    when i used gaussian elimination i found that on the 3rd equation near the bottom that 0= 8, which shows its inconsistant.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member Glaysher's Avatar
    Joined
    Aug 2006
    From
    Newton-le-Willows
    Posts
    224
    My graphical calculator has checked my previously posted answer but I won't repost it until I know for sure that this isn't part of the Challenge
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Glaysher
    Just noticed that you're from Australia. This isn't part of the Australian Maths Challenge is it?
    His profile says he a 2nd year undergrad, so not eligable, so you can
    go ahead and answer.

    RonL
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member Glaysher's Avatar
    Joined
    Aug 2006
    From
    Newton-le-Willows
    Posts
    224
    See attached
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,689
    Thanks
    617
    Hello, sterps!

    Yes, Gaussian elimination is a good approach.
    (You must have made some errors, though.)


    Three planes have equations: . \begin{array}{ccc}x+3y-z \:= \:4\\ 2x+8y \:=\:18 \\x-y-3z \:=\:\text{-}6\end{array}

    a) have no common point of intersection
    b) intersect in a point
    c) intersect in a line
    d) intersect in a plane

    We have: . \begin{pmatrix}1 & 3 & \text{-}1 & | & 4\\ 2 & 8 & 0 & | & 18\\ 1 & \text{-}1 & \text{-}3 & | & \text{-}6\end{pmatrix}

    . . . . \begin{array}{cccc} \\ \frac{1}{2}R_2\\ \\\end{array}\;\begin{pmatrix}1 & 3 & \text{-}1 & | & 4\\1 & 4 & 0 & | & 9 \\ 1 & \text{-}1 & \text{-}3 & | & \text{-}6\end{pmatrix}

    \begin{array}{ccc} \\ R_2-R_1\\ R_3 - R_1\end{array}\;\begin{pmatrix}1 & 3 & \text{-}1 & | & 4\\ 0 & 1 & 1 & | & 5\\0 & \text{-}4 & \text{-}2 & | &\text{-}10\end{pmatrix}

    \begin{array}{ccc}R_1-3R_2\\ \\ R_3+4R_2\end{array}\;\begin{pmatrix}1 & 0 & \text{-}4 & | & \text{-}11 \\ 0 & 1 & 1 & | & 5\\ 0 & 0 & 2 & | & 10\end{pmatrix}

    . . . . \begin{array}{ccc} \\ \\ \frac{1}{2}R_3\end{array}\;\begin{pmatrix}1 & 0 & \text{-}4 & | & \text{-}11\\0 & 1 & 1 & | & 5\\ 0 & 0 & 1 & | & 5\end{pmatrix}

    . \begin{array}{cccc} R_1+4R_3 \\ R_2-R_3 \\ \\ \end{array}\;\begin{pmatrix}1 & 0 & 0 & | & 9 \\ 0 & 1 & 0 & | & 0\\0 & 0 & 1 & | & 5\end{pmatrix}


    Therefore: (b) The planes intersect in a point, \bf{(9,0,5)}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vectors - Lines and Planes Question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: April 16th 2010, 06:07 PM
  2. Lines and Planes Question
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: December 9th 2009, 11:50 AM
  3. Lines and Planes in space Question?
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: July 28th 2008, 02:11 PM
  4. Lines and planes question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 8th 2008, 03:35 PM
  5. Planes, lines, points
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 2nd 2008, 05:19 PM

Search Tags


/mathhelpforum @mathhelpforum