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Homework Help: 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:


    Equation of the line:


    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





    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 = 0

    y = 4

    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


    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.
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