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Show that four points lie on a plane

  1. Aug 8, 2014 #1
    1. The problem statement, all variables and given/known data
    (2; 0; 1); (-1; 2; 3); (3; 2; 2) and (3;-6;-3)

    2. Relevant equations

    PS→⋅(PR→×PQ→)=0

    3. The attempt at a solution

    Hi all, I am just wondering if my calculations are correct, and in fact these points do not lie on a plane. My answer is = 50 and i am not confident. Can anyone help me please?
     
    Last edited by a moderator: Aug 8, 2014
  2. jcsd
  3. Aug 8, 2014 #2

    Orodruin

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    It would be much easier to judge if what you are doing is correct if you actually showed us what you are doing.

    Edit: Also, the points do lie in a plane - any solution not resulting in this is going to be wrong.
     
    Last edited: Aug 8, 2014
  4. Aug 8, 2014 #3

    ehild

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    What is 50?

    ehild
     
  5. Aug 8, 2014 #4
    I have miss-read the question. All it is asking me to do, is prove that these points lie in the same plane. May i ask how?
     
  6. Aug 8, 2014 #5

    Orodruin

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    If this is a homework problem or problem in a course you are taking there should be a description of how to determine this in your course literature. Have you tried applying that?
     
  7. Aug 8, 2014 #6

    HallsofIvy

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    You have the answer in your first post:
    PS→⋅(PR→×PQ→)=0
    (I assume the arrow after indicates "vector")

    Any three points, such as P, Q, and R must lie in a plane so the two vectors PR and PQ lie in a plane and their cross product is perpendicular to the plane. The fourth point, S, lies in that same plane if and only the vector PS does also- and then its dot product with the perpendicular vector is 0.
     
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