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Math Help - a normal vector to the plane

  1. #1
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    a normal vector to the plane

    this question is easy but i've forgotten how to answer it.

    a plane contains the points A(0,1,5),B(-3,2,4) and C(5,3,-4).find a normal vector to the plane.

    thank you.
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  2. #2
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    Quote Originally Posted by kokolily View Post
    this question is easy but i've forgotten how to answer it.

    a plane contains the points A(0,1,5),B(-3,2,4) and C(5,3,-4).find a normal vector to the plane.

    thank you.

    Way 1 find a standard form ax+by+cz+d=0 for the plane containing the above vectors, and then (a,b,c) is normal to each and every once of them.

    Way 2: (this is a slight variation of the above): let \overrightarrow{AB}=(-3,1,-1)\,,\,\overrightarrow{AC}=(5,2,-9) , and now calculate the vector (-3,1,-1)\times (5,2,-9) , which is normal to the plane generated by \overrightarrow{AB}\,,\,\overrightarrow{AC} .

    Tonio
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