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Math Help - Plane M

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    Plane M

    I am looking a proof for next thing:

    If M is a plane that passing through the axis so there are a,b,c who belonging to R, so that:
    M={(x,y,z)in R^3 | ax+by+cz=0}
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  2. #2
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    Quote Originally Posted by Also sprach Zarathustra View Post
    I am looking a proof for next thing:

    If M is a plane that passing through the axis so there are a,b,c who belonging to R, so that:
    M={(x,y,z)in R^3 | ax+by+cz=0}

    מממ...אני מכיר את השאלה הזאת מתרגיל באלגברה לינארית מהאוניברסיטה העברית

    This is plane analytic geometry: there exists a normal vector (a,b,c) to the plane "tailed" or "kashur" to the origin in \mathbb{R}^3, and thus it has the formal above: scalar product (a,b,c)\cdot (x,y,z)=0\Longrightarrow ax+by+cz=0.

    Of course, the above depends on how you've defined a plane in space...

    Tonio
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