1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help needed with 3d geometry problem: important

  1. Jul 9, 2011 #1
    help needed with 3d geometry problem: important!!!!

    1. The problem statement, all variables and given/known data

    find the equations of the two planes through the origin which are parallel to the line
    (x - 1)/2 = (-y-3) = (-z-1)/2
    and at a distance of 5/3 from it. also, show that the planes are perpendicular

    2. Relevant equations



    3. The attempt at a solution

    my attempt at the solution

    plane equations passing through (0,0,0) are ax+by+cz=0 (&) a'x+b'y+c'z=0
    now, 2.a - b - 2.c = 0 (since direction ratios of given line is perpendicular to the normal of the plane)
    also by distance formula (a.(1) + b.(-3) +c.(-1))/(a^2 + b^2 + c^2)^(1/2) = 5/3
    the a - 3.b - c = 5/3 (since a^2 + b^2 + c^2 = 1)
    and now i am stuck........

    FYI : [the answer is 2x+2y+z=0; x-2y+2z=0]
     
  2. jcsd
  3. Jul 9, 2011 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: help needed with 3d geometry problem: important!!!!

    You have got the equations you need to find the normals. 2*a-b-2*c=0, a-3*b-c=5/3 and a^2+b^2+c^2=1. If you solve those will get normals for the two planes. The books answer doesn't assume a^2+b^2+c^2=1 so be prepared to multiply the normal by a constant to get the books answers.
     
  4. Jul 10, 2011 #3
    Re: help needed with 3d geometry problem: important!!!!

    the problem is the equations are unsolvable

    2*a - b - 2*c = 0
    the we get (a - c) = b/2
    substitute this in a - 3*b - c =5/3
    we get b = -2/3
    now substitute b = -2/3 in a^2 + b^2 + c^2 = 1
    we get a^2 + c^2 = -1/3 !!!!!!!!!!!!!!!!!!!
     
  5. Jul 10, 2011 #4
    Re: help needed with 3d geometry problem: important!!!!

    this means that my basic equations are wrong.. i am missing a conceptual link here.. please help....!!!!!!!!!!!!!
     
  6. Jul 10, 2011 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Re: help needed with 3d geometry problem: important!!!!

    No, you don't get this. You should get a^2 + c^2 = 1 - (2/3)^2 = 5/9.

    RGV
     
  7. Jul 10, 2011 #6
    Re: help needed with 3d geometry problem: important!!!!

    ooops .. sorry .. you are right ..

    let me sum up this situation in an equation....

    sleepless night + math => (2/3)^2 = (4/3)

    thanks dude...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help needed with 3d geometry problem: important
  1. Geometry Help Needed! (Replies: 6)

  2. Geometry help needed (Replies: 0)

Loading...