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Math Help - Equation of a plane parallel to two vectors.

  1. #1
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    Equation of a plane parallel to two vectors.

    A plane goes trough a point and is parallel to two vectors what is the general equation?

    The plane goes trough the point [2,3,1] and is parallel to the two vectors [1,2,3] and [2,3,-1].

    The answer is 11x-7y+z-2=0

    If I do the cross product of the two vectors I get the vector [-11,7,-1] which if multiplied by -1 corresponds to the answer but I dont thin that's the right way. :P
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    MHF Contributor FernandoRevilla's Avatar
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    Re: Equation of a plane parallel to two vectors.

    Hint (1,2,3)\times (2,3,-1)=(-11,7,-1) .
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    Re: Equation of a plane parallel to two vectors.

    Well that's what I've done so far but I dont know how to proceed. How do I turn the resulting vector in to a normal equation?
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    MHF Contributor FernandoRevilla's Avatar
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    Re: Equation of a plane parallel to two vectors.

    Quote Originally Posted by dipsy34 View Post
    Well that's what I've done so far but I dont know how to proceed. How do I turn the resulting vector in to a normal equation?
    -11(x-2)+7(y-3)-(z-1)=0
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    Re: Equation of a plane parallel to two vectors.

    Quote Originally Posted by dipsy34 View Post
    Well that's what I've done so far but I dont know how to proceed. How do I turn the resulting vector in to a normal equation?
    If U~\&~V are two non-parallel vectors and P is a point. Let R=<x,y,z> then (U\times V)\cdot(R-P)=0 is a plane parallel to the vectors that contains the point.
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