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!

Plane intersections

  1. May 7, 2010 #1
    1. The problem statement, all variables and given/known data

    Find out if the following planes and lines intersect. If they intersect, state the point of intersection

    Plane: 2x + y + 3z = 10
    Line: Passing through the point A(1, 5, 1) and B(0, 4, 2)


    2. Relevant equations



    3. The attempt at a solution
    I have solved the problem, but am unsure if my working/result is correct..

    first we have to find the equation for the line:

    [x,y,z]=(0,4,2)+t[1,5,1]

    Equation of the line:

    x=1t
    y=4+5t
    z=2+t

    We have to know check if they intersect:

    2x + y + 3z = 10

    Substitute the line equation in the line :
    2(t)+(4+5t) + 3(2+t) = 10

    2t+4+5t+6+3t=10

    10t+10=10

    10t=0

    t=0

    The lines and the plane intersect, since t is a number (0).

    Find the point of intersection

    Substitute the value of t into the parametric equations:

    x=1(0)
    x = 0

    y=4+5(0)
    y = 4

    z=2+(0)
    z = 2


    so the point of intersection is (0,4,2)..but this is the point given in the original question..I am very confused over here...any help is much appreciated

    Thanks! :smile:
     
  2. jcsd
  3. May 7, 2010 #2

    Mark44

    Staff: Mentor

    This isn't right. You can't just take the two points and plunk them into your parametric equation. You need to find a vector with the same direction as the line. Use the two given points to do this.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook