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Lines And Planes Query

  1. Sep 3, 2006 #1
    Help!!!!!!!!!

    Hi everyone,
    This is my very first post on physics forum! I was wondering if anyone could help explain to me how to find the coordinates of a point where a line intersects a plane.
    The question i'm trying to do has given the line as r= (2, 7, -5) + t(1, 2, -1) and the plane as 2x + 3y - z=3.
    Any advice or help would be much appreciated, thank you.
     
    Last edited: Sep 3, 2006
  2. jcsd
  3. Sep 3, 2006 #2

    Galileo

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    The x,y and z coordinates of the points on the line are (2+t, 7+2t, -5-t) right?
    Now those coordinates have to satisfy 2x+3y-z=3 to be in the plane. Just plug it in and see for what value it t they are.
     
  4. Sep 3, 2006 #3

    HallsofIvy

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    Saying the line is given by the vector equation r= (2,7,-5)+ t(1, 2, -1) is the same as saying it is given by the parametric equations x= 2+ t, y= 7+ 2t, z= -5- t. Replace x, y, z in the equation of the plane to get an equation for t and solve.
     
  5. Sep 3, 2006 #4

    Hootenanny

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    Hi there E=mc2 and welcome to PF,

    According to the rules of this forum, you must show some of your own efforts in order to gain assistance. However, if I may offer you the hint that any point of intersection must satisfy the equation of both the line and plane.

    Edit: Halls beat me to it; I must learn to type faster. :smile:
     
  6. Sep 3, 2006 #5

    Hootenanny

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    Please don't double post E=mc2.
     
  7. Sep 3, 2006 #6
    Thanks alot guys, i really appreciate it. Sorry about the double post Hootenanny and beleive me i made some effort but yeah didn't really show it, sorry about that. Won't happen again.
    Thank you again.
     
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