Results 1 to 3 of 3

Math Help - Vector equation of a line of intersection of three planes

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    33

    Vector equation of a line of intersection of three planes

    I have been given a system of equations that appears below:
    2x - 7y + 5z = 1
    6x + 3y - z = -1
    -14x - 23y + 13z = 5
    I am told to find an vector equation of the line that is formed by the intersection of these three planes. I could use some step by step instructions, or a link to a resource that explains it well, because as of yet I have found nothing.

    Thanks,
    Peter
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Quote Originally Posted by flybynight View Post
    I have been given a system of equations that appears below:
    2x - 7y + 5z = 1
    6x + 3y - z = -1
    -14x - 23y + 13z = 5
    I am told to find an vector equation of the line that is formed by the intersection of these three planes. I could use some step by step instructions, or a link to a resource that explains it well, because as of yet I have found nothing.

    Thanks,
    Peter
    I would start by solving the coefficient matrix. You will end up with that z is a free variable.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,696
    Thanks
    1467
    Quote Originally Posted by flybynight View Post
    I have been given a system of equations that appears below:
    2x - 7y + 5z = 1
    6x + 3y - z = -1
    -14x - 23y + 13z = 5
    I am told to find an vector equation of the line that is formed by the intersection of these three planes. I could use some step by step instructions, or a link to a resource that explains it well, because as of yet I have found nothing.

    Thanks,
    Peter
    Is the intersection a line? Normally, two planes intersect in a line so that three planes intersect at a point- with three equations you can solve for specific values of x, y, and z. Presumably, these equations are not "independent". If you don't want to use matrices as dwsmith suggests, try solving the three equations. If they really are not independent, you will find that you cannot solve for x, y, and z but can solve for two of the unknown values in terms ofthe third. Use that write the equation of the line using that third value as parameter.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 22nd 2010, 02:46 AM
  2. Intersection line of planes, Vector geometry
    Posted in the Geometry Forum
    Replies: 7
    Last Post: April 1st 2010, 07:59 AM
  3. Intersection line of planes, Vector geometry
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: April 1st 2010, 02:29 AM
  4. Intersection line of planes, vector geometry problem
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 31st 2010, 07:02 AM
  5. Equation of the Line of Intersection of two Planes Help
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: June 10th 2008, 10:49 AM

Search Tags


/mathhelpforum @mathhelpforum