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!

Line/plane thing

  1. Nov 3, 2008 #1
    1. The problem statement, all variables and given/known data
    Given some plane, [tex]3x+2y-z=6[/tex], and a point [tex](2,3,6)[/tex]

    Find a line in the plane passing through that point.

    2. Relevant equations

    3. The attempt at a solution
    I tried finding the vector perpendicular to the plane, [tex]<3,2,-1>[/tex], but I'm not sure what to do with it.
  2. jcsd
  3. Nov 3, 2008 #2
    A line passing through two points [itex]\vec{r_0}[/itex] and [itex]\vec{r_1}[/itex] is simply

    [tex] \vec{r}=(1-t)\vec{r_0}+t\vec{r_1}[/tex]

    You are given a point that you want the line through and you can figure out another arbitrary one right?
  4. Nov 3, 2008 #3


    User Avatar
    Homework Helper

    You could use this as the direction of the line that you want.

    EDIT: Read the question wrong, I thought it asked for a line passing through that point and not necessarily contained in the plane.
    Last edited: Nov 4, 2008
  5. Nov 4, 2008 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    No, you cannot! That vector is perpendicular to the plane while the line you want is in the plane. The normal vector doesn't help at all. As jeffreydk said, a line is determined by two points. You are already given one point in the plane (did you check that it actually is in the plane?) Now choose any other point in the plane (take what ever values you like for x and y and solve for z) and use those two points to determine the line. There are, of course, an infinite number of solutions.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Line/plane thing
  1. Lines and planes (Replies: 5)