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Math Help - Equations of Planes

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    Equations of Planes

    Find the scalar equation of the plane that passes through the origin and the line of intersection of the planes 3x+4y-7z-2=0 and 2x+3y-4=0
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    Quote Originally Posted by skeske1234 View Post
    Find the scalar equation of the plane that passes through the origin and the line of intersection of the planes 3x+4y-7z-2=0 and 2x+3y-4=0
    Any plane that passes through the line of intersection of the planes 3x+4y-7z-2=0 and 2x+3y-4=0 can be written as:

    (3x+4y-7z-2)+\alpha(2x+3y-4)=0 --------(1)

    Since this plane passes through the origin,

    -2+\alpha(-4)=0

    \alpha=-\frac{1}{2}

    Substituting in (1),

    (3x+4y-7z-2)-\frac{1}{2}(2x+3y-4)=0

    6x+8y-14z-4-2x-3y+4=0

    4x+5y-14z=0
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