Results 1 to 2 of 2

Math Help - Line of Intersection of Planes

  1. #1
    Junior Member Morphayne's Avatar
    Joined
    May 2008
    Posts
    31

    Exclamation Line of Intersection of Planes

    Problem:

    Find parametric and symmetric equations of the line of intersection of the two planes.

    2x+y+z-5=0 and 3x+2y+2z-8=0

    Answers:

     x=2
     y=t
     z=1-t

    No symmetric equations.

    Comments:

    I'm stuck on this one.
    I tried multiplying the first equation by -2 and did the elimination to solve for y or z but I get messed up.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Morphayne View Post
    Problem:

    Find parametric and symmetric equations of the line of intersection of the two planes.

    2x+y+z-5=0 and 3x+2y+2z-8=0

    Answers:

     x=2
     y=t
     z=1-t

    No symmetric equations.

    Comments:

    I'm stuck on this one.
    I tried multiplying the first equation by -2 and did the elimination to solve for y or z but I get messed up.
    Two equations and three unknowns so infinite number of solutions (therefore there's a parameter). There are an infinite number of ways of expressing the answer. One such is to start by letting y = t, say, where t is any real number.

    Then:

    2x + z = 5 - t .... (1)

    3x + 2z = 8 - 2t .... (2)

    Solve (1) and (2) simultaneously for x and z in terms of t. I suggest 2 (1) - (2):

    x = 2.

    Now substitute x = 2 into (1) and solve for z.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Angle between planes and line of intersection of planes.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 6th 2011, 12:08 PM
  2. Line of Intersection between two planes
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: June 23rd 2011, 06:15 PM
  3. Line of intersection of two planes
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: June 7th 2010, 02:00 AM
  4. Line of intersection of 3 planes.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 26th 2008, 11:13 AM
  5. line of intersection of planes
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 16th 2008, 03:39 AM

Search Tags


/mathhelpforum @mathhelpforum