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Equation of a Plane with 2 Points and Perpendicular

  1. Mar 18, 2008 #1
    1. The problem statement, all variables and given/known data

    Determine the equation of the plane that contains the points A(1, 2, 3) and B(2, 3, -1) and is perpendicular to the plane 3x + y + z + 1=0. I think I know how to do it with only one point, not two

    3. The attempt at a solution

    I know that v= normal so it would be (3, 1, 1). Then I could use point A and say (x-1, y-2, z-3)dot(3, 1, 1)=0
    After expanding, I get 3x + y + z -8=0. Do I need to incorporate the other point?
     
  2. jcsd
  3. Mar 18, 2008 #2

    Vid

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    No, you only need to use one point. Notice that if you had used the other point, you would have gotten the same equation.
     
  4. Mar 18, 2008 #3
    the answer in the book is 5x-13y-2z+27=0. Does it make sense that my answer is so different? Would they give the same answer?
     
  5. Mar 18, 2008 #4

    Vid

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    Your normal vector is wrong. (3,1,1) is perpendicular to the given plane, but not the plane they want.
     
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