Results 1 to 5 of 5

Math Help - 2 Intersecting 3-D planes

  1. #1
    Newbie DerekZ10's Avatar
    Joined
    Jan 2011
    Posts
    12

    2 Intersecting 3-D planes

    2 Intersecting 3-D planes-scan0001.jpg

    I have been at this same problem for a few hours now. The scan of the paper is above. I'm trying to find the parametric and symmetric equations for the line of intersection for the planes:

    3x - 3y - 7z = -4 and x - y + 2z = 3.

    I thought I had it solved but if i plug the parametric equations into the original equations neither comes out right. It would if one of the signs where different for the 13t in the parametric equations. But I don't know where I dropped it.

    Please help find my mistake or what I'm doing wrong.

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie DerekZ10's Avatar
    Joined
    Jan 2011
    Posts
    12

    Re: 2 Intersecting 3-D planes

    nvm I messed up on the sign in the cross products.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1597
    Awards
    1

    Re: 2 Intersecting 3-D planes

    Quote Originally Posted by DerekZ10 View Post
    Click image for larger version. 

Name:	scan0001.jpg 
Views:	17 
Size:	781.8 KB 
ID:	22508
    equations for the line of intersection for the planes:
    3x - 3y - 7z = -4 and x - y + 2z = 3.
    I thought I had it solved but if i plug the parametric equations into the
    Can you show that the point (1,0,1) is on both planes?
    The direction vector is: <3,-3,-7>\times<1,-1,2>.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466

    Re: 2 Intersecting 3-D planes

    I would think that a rather obvious thing to do would be to subtract 3 times the second equation from the first:
    (3x- 3y- 7z)- 3(x- y+ 2z)= -4- 3(3)
    -13z= -13 so that z= 1, a constant.

    With z= 1, the two equations become 3x- 3y- 7= -4 and x- y+ 2= 3 which both reduce to x- y= 1.
    x= y+ 1. Using y as parameter, x= t+1, y= t, z= 1 are parametric equations for the line of intersection.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie DerekZ10's Avatar
    Joined
    Jan 2011
    Posts
    12

    Re: 2 Intersecting 3-D planes

    Is there possibly 2 answers? I went with x = 1 - 13t, y = -13t, and z = 1. Substitution of those worked on both equations. My original mistake was that I dropped neg sign on y = 13t.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Intersecting planes
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: August 27th 2011, 09:19 AM
  2. Parallel planes and intersecting planes
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 8th 2010, 08:25 AM
  3. 3D: 2 planes intersecting
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 25th 2010, 07:24 PM
  4. Intersecting Planes
    Posted in the Calculus Forum
    Replies: 11
    Last Post: August 11th 2008, 01:14 PM
  5. Intersecting Planes
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 2nd 2008, 12:08 AM

/mathhelpforum @mathhelpforum