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3D Plane question

  1. Mar 29, 2004 #1
    I have a unit test on 3D-Planes coming up!! And I was wondering if in 3D, a line and a plane intersect at a single point. How would you determine the equation of the reflection of the line in the plane?
    Please try to provide the steps. Thanks!
     
  2. jcsd
  3. Mar 29, 2004 #2
    Yes, a plane and a line intersect in one point. Let's say you have the plane:
    [tex]\pi : 7x + 8y + 9z + 10 = 0[/tex]
    And the line:
    [tex]\underline{l} = (1, 2, 3) + t(4, 5, 6)[/tex]
    You know that the X, Y and Z coordinates of every point on the line are:
    [tex]x = 1 + 4t[/tex]
    [tex]y = 2 + 5t[/tex]
    [tex]z = 3 + 6t[/tex]
    Substitute these in the equation of the plane and you will get:
    [tex]7(1 + 4t) + 8(2 + 5t) + 9(3 + 6t) + 10 = 0[/tex]
    One unknown - t. Find it and you can find the coordinates of the intersection point.
     
  4. Mar 29, 2004 #3
  5. Mar 29, 2004 #4
    really appreciate it, this was helpful! thanks!
     
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