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!

Intersection of 3 planes

  1. Jan 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Find value of k so that
    x+2y-z=0
    x+9y-5z=0
    kx-y+z=0
    intersect in a line

    2. Relevant equations



    3. The attempt at a solution
    multiply l1 by 5
    subtract l2 from 5l1
    end up with:
    4x+y=0

    subtract l1 from l2
    end up with:
    7y-4z=0

    i have no idea what to do from here, or even if what i did was correct.
    thanks for the help.
     
  2. jcsd
  3. Jan 21, 2009 #2

    rock.freak667

    User Avatar
    Homework Helper

    Rewrite it in maxtrix form and row-reduce until echelon form is obtained. For the planes to intersect in a line, then when you reduce in echelon form, the rank of the augmented matrix should be less than 3 (the number of variables)
     
  4. Jan 21, 2009 #3
    ahh thank you.

    i have another problem:

    Find the vector equation of the plane through A(1,-7,-2) and perpendicular to line (5,0,0)+t(2,0,7)

    i have parametric equations of the line
    x=5+t
    y=0
    z=7t

    what do i do from here?
     
  5. Jan 21, 2009 #4

    rock.freak667

    User Avatar
    Homework Helper

    If the line is perpendicular to the plane, what can you say about the normal to the plane and the line?
     
  6. Jan 21, 2009 #5
    line is normal to the plane?
     
  7. Jan 21, 2009 #6
    ok, i found took the vector from 5,0,0 from 1,-7,-2

    i made the z component of the vector 0

    then knowing that the dot product of the line and a vector of the plane is 0, i found the component of z of a vector of the plane which would make it perpendicular to the line

    is that possible?
     
  8. Jan 21, 2009 #7

    rock.freak667

    User Avatar
    Homework Helper

    Yes, so for a vector line in the for r=a+tu, where u is the direction of the line.

    In your example u=<2,0,7>, if the lines is perpendicular to the plane, then so is the direction.

    So if the direction (u) is normal to the plane, doesn't that mean that the vector u is parallel to the normal?
     
  9. Jan 21, 2009 #8
    absolutely
     
  10. Jan 21, 2009 #9

    rock.freak667

    User Avatar
    Homework Helper

    so if it is parellel to the plane then

    Q<2,0,7> would be a normal to this plane. Pick any non-zero value for Q, and you'll get the normal to the plane,N. When you get that, use the formule

    [tex](\vec{r}-\vec{r_0})\cdot \vec{N}=0[/tex]

    Where [itex]\vec{N}[/itex] is the normal vector and [itex]r_0[/itex] is a point on the plane (which you were given in the question).
     
    Last edited: Jan 21, 2009
  11. Jan 21, 2009 #10
    what is the other r in the question?
     
  12. Jan 21, 2009 #11

    rock.freak667

    User Avatar
    Homework Helper

    that is just <x,y,z>

    so that for the point <x0,y0,z0>

    [tex]\vec{r}- \vec{r_0} = <(x-x_0),(y-y_0),(z-z_0)>[/tex]
     
  13. Jan 21, 2009 #12
    thank you.

    i have another question:



    find a vector equation of the line through the point 4,5,5

    that meets the line: (x-11)/3=y+8=z-4

    i dont even know where to start on this one.

    perhaps i do the same thing as before?

    find the vector between 4,5,5 and the point on the line when t=0? (starting point?)
    then set one of the components to 0 and use the dot product formula?
     
    Last edited: Jan 21, 2009
  14. Jan 21, 2009 #13

    rock.freak667

    User Avatar
    Homework Helper

    For a vector line written in the form

    [tex]\frac{x-a}{p} = \frac{y-b}{q}= \frac{z-c}{r}[/tex]

    What does <a,b,c> represent and what does <p,q,r> represent?
     
  15. Jan 21, 2009 #14
    -a, -b, -c is a point
    p, q, r are components in the x, y, z axis
     
  16. Jan 21, 2009 #15

    rock.freak667

    User Avatar
    Homework Helper

    Good
    <p,q,r> would be the direction of the line.
     
  17. Jan 21, 2009 #16
    haha where do i go from there then? btw is my process that i edited in at 2:27 am correct?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Intersection of 3 planes
  1. Intersecting planes (Replies: 10)

Loading...