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Math Help - Finding A Particular Equation

  1. #1
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    Finding A Particular Equation

    "Describe and find an equation for the surface generated by all points (x,y,z) that are four units from the plane 4x - 3y + z = 10."

    Firstly, I found a point P on the plane: P = (0,0,10). Then I constructed a vector whose initial point is (0,0,10) and terminal point is Q = (x,y,z):

    \Large\vec{PQ} = \langle x, y,z-10 \rangle

    The vector normal to the plane is \vec{n} = \langle 4,-3,1 \rangle

    D = 4 = \frac{|\langle x,y,z-10 \rangle \cdot \langle 4,-3,1 \rangle|}{\sqrt{26}} \implies 4\sqrt{26} + 10 = 4x - 3y + z

    Does this appear to be the correct answer?
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  2. #2
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    Re: Finding A Particular Equation

    Quote Originally Posted by Bashyboy View Post
    "Describe and find an equation for the surface generated by all points (x,y,z) that are four units from the plane 4x - 3y + z = 10."

    Firstly, I found a point P on the plane: P = (0,0,10). Then I constructed a vector whose initial point is (0,0,10) and terminal point is Q = (x,y,z):

    \Large\vec{PQ} = \langle x, y,z-10 \rangle

    The vector normal to the plane is \vec{n} = \langle 4,-3,1 \rangle

    D = 4 = \frac{|\langle x,y,z-10 \rangle \cdot \langle 4,-3,1 \rangle|}{\sqrt{26}} \implies 4\sqrt{26} + 10 = 4x - 3y + z

    Does this appear to be the correct answer?
    No it does not. Almost, but not correct. You just cannot drop the absolute values.

    If A=|B| then B=\pm A~.
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  3. #3
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    Re: Finding A Particular Equation

    Note that there are two planes that are a given distance from a given distance.
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