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Math Help - vector equation of plane

  1. #1
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    Smile vector equation of plane

    Hello.. I need help with vector equation!!!

    Find the vector equation of the plane that passes through the points (1,2,7), (2,3,4) and (-1,2,1)

    I know how to work out with the two pionts but not three

    THANKYOU FOR HELPING ME = )
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sinni8 View Post
    Hello.. I need help with vector equation!!!

    Find the vector equation of the plane that passes through the points (1,2,7), (2,3,4) and (-1,2,1)
    see example 1 here

    I know how to work out with the two pionts but not three
    no you don't ...it can't be done

    and if you could, why didn't you just ignore the third point and do it?
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    see example 1 here

    no you don't ...it can't be done

    and if you could, why didn't you just ignore the third point and do it?
    No i cant what i mean is i can find the vector equation of plane with there are two points such as (1,2,1) and (2,3,5) but Since i have three points i need to the other method which is i cant do it!!
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  4. #4
    o_O
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    A plane can be defined as: a(x - x_{0}) + b(y - y_{0}) + c(z - z_{0}) = 0

    where (x_0, y_0, z_0) is a point on the plane and (a,b,c) is the normal vector.

    Let points A, B, C be (1,2,7), (2,3,4) and (-1,2,1) respectively.

    Notice that the plane contains vectors \overrightarrow{AB} and \overrightarrow{AC} and their cross product will give the normal vector perpendicular to it.

    So find \overrightarrow{AB} \times \overrightarrow{AC} to get (a,b,c) and use one of A, B, or C for your (x_{0}, y_0, z_0).

    Now, again, plug it all into: a(x-x_0) + b(y-y_0) + c(z-z_0) = 0
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sinni8 View Post
    No i cant what i mean is i can find the vector equation of plane with there are two points such as (1,2,1) and (2,3,5) but Since i have three points i need to the other method which is i cant do it!!
    you cannot, repeat, cannot find the vector equation of a plane if all you are given are two points in the plane. you need more information. see the link i gave you, it goes through a problem exactly like this one. take a gander at o_O's post as well.
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