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Math Help - Equation of plane & normal vector

  1. #1
    Junior Member
    Joined
    Jun 2009
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    Equation of plane & normal vector

    OK so if the equation of a plane is ax + by + cz = d you can just read off that the normal vector is (a,b,c)... but why is this? Is there a geometric kind of argument for why it's like that, or is it just a handy co-incidence?

    Thanks
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  2. #2
    Senior Member
    Joined
    Jul 2009
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    Hi Aileys.

    It's not a coincidence. In vector, \left(\begin{array}{cc}x\\y\\z\end{array}\right) usually denoted by \vec r

    So, ax+by+cz=d can be written as :

    \left(\begin{array}{cc}x\\y\\z\end{array}\right) \cdot \left(\begin{array}{cc}a\\b\\c\end{array}\right) = d

    \vec r \cdot \left(\begin{array}{cc}a\\b\\c\end{array}\right) = d

    That's a general equation of plane where \left(\begin{array}{cc}a\\b\\c\end{array}\right) is the normal vector
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