1. Not finding help here? Sign up for a free 30min 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!

Finding solution for three sets of planes

  1. Apr 22, 2015 #1
    1. The problem statement, all variables and given/known data
    (I did not copy the problem statement, but basically solve the system of equations if there is solution and give a geometrical interpretation)

    P1: 2x - y + 6z = 7
    P2: 3x + 4y + 3z = -8
    P3: x - 2y - 4z = 9

    2. Relevant equations

    Scalar triple product: n1(n2 × n3)

    3. The attempt at a solution
    (Step 1): Checked that they are not parallel

    (Step 2): Checked that they are not coplanar

    (Step 3): Find the unique solution
    R2 - 3R3
    ⇒ 0x + 10y + 15z = -35
    ⇒ 6y + 9z = -21
    R1 - 2R3
    ⇒ 0x + 3y + 14z = -11
    ⇒ 6y + 28z = -22

    ⇒ -21 - 9z = -22 - 28z
    ⇒ z = -1/19
    ⇒ y = -65/19
    ⇒ x = 37/19

    (Edited: i double checked values for y & x)

    Although the answer is that they intersect at (3, -5, 1)
     
    Last edited: Apr 22, 2015
  2. jcsd
  3. Apr 22, 2015 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    It looks to me like the part you left out (the actual problem statement) was the crucial part.

    If the equations really are
    P1: 2x - y + 6z = 7
    P2: 3x + 4y + 3z = -8
    P3: x - 2y - 4z = 9

    Then x= 3, y= -5, z= 1 clearly is not the solution!
    2(3)- (-5)+ 6(1)= 6+ 5+ 6= 17 NOT 7.

    Since (3, -5, 1) do satisfy the other two equations, I suspect you have the first equation wrong.
     
  4. Apr 22, 2015 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Did you try substituting the given answer in the three plane equations? I think you will discover a typo.

    Edit: strange... On two threads, I see a post by Halls posted half an hour before mine that wasn't visible to me until half an hour after mine.
     
    Last edited: Apr 22, 2015
  5. Apr 22, 2015 #4
    Thank you!!! I re-did the question where the equation for my first plane is 2x - y + 6z = 17 and I got the answer :D
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Finding solution for three sets of planes
  1. Find the solution set (Replies: 3)

Loading...