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  1. #1
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    Finding the equation of the plan. Mediator of the segment of extreme A(1,-2,6) and B(3,0,0)



    Answer:
    x+y-3z+8=0
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi
    Quote Originally Posted by Apprentice123 View Post
    Finding the equation of the plan. Mediator of the segment of extreme A(1,-2,6) and B(3,0,0)

    Answer:
    x+y-3z+8=0
    To find the answer you need to know two things :
    • the mediating plane is orthogonal to the line segment [AB] (this boils to saying that the plane is orthogonal to \vec{AB})
    • the midpoint of [AB] is a point of the mediating plane.
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  3. #3
    Moo
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    Hello,

    Quote Originally Posted by Apprentice123 View Post
    Finding the equation of the plan. Mediator of the segment of extreme A(1,-2,6) and B(3,0,0)



    Answer:
    x+y-3z+8=0
    A mediator is perpendicular to the segment and passes throught the midpoint.

    The coordinates of \overrightarrow{AB} are (2~,~2~,~-6)

    So the equation of the plan, which has AB as orthogonal vector, will be :

    2x+2y-6z+d=0

    -----------------
    With d to determine. And for this, you will have to use the fact that it goes throught the midpoint of AB.

    Coordinates of the midpoint of [AB] : \left(\frac{3+1}{2}~,~\frac{-2+0}{2}~,~\frac{6+0}2\right), that is to say (2~,~-1~,~3).

    This point is on the plane, so substitute and get d.

    After that, divide the equation by 2.
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  4. #4
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    Thank you
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