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Thread: More Planes

  1. #1
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    More Planes

    Find an equation of a plane that is perpendicular to the plane x-2y+z=7

    I know his has to do with vectors because the dot product must = 0....
    :-/
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  2. #2
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    There is more than one answer to this problem.
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  3. #3
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    Hello, stones44!

    Find an equation of a plane that is perpendicular to the plane $\displaystyle x-2y+z\:=\:7$
    There is an infinite number of answers . . .
    A door is perpendicular to the floor. .Swing the door
    . . and you have thousands of planes perpendicular to the floor.

    Our plane can go through any point, say, $\displaystyle P(5,\,6,\,7)$

    Its normal vector, $\displaystyle \vec{n} \:=\:\langle a,\,b,\,c\rangle$, must be perpendicular to $\displaystyle \langle 1,\,\text{-}2,\,1\rangle$

    Hence, we have: .$\displaystyle a - 2b + c \:=\:0$

    . . We can use, for example: .$\displaystyle \vec{n} \:=\:\langle3,\,2,\,1\rangle$


    The equation is: .$\displaystyle 3(x-5) + 2(y-6) + 1(z-7)\:=\:0$

    . . . . . . . . . . . . $\displaystyle \boxed{3x + 2y + z \:=\:34}$

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