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Thread: 3D vectors and planes

  1. #1
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    3D vectors and planes

    Find the equation for the plane through P(1,e,pi) perpendicular to the vector from the origin to P.
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  2. #2
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    Hello, ineedhelp!

    Exactly where is your difficulty?


    Find the equation for the plane through $\displaystyle P(1,\,e,\,\pi)$
    perpendicular to the vector from the origin to $\displaystyle P.$

    We are given a point on the plane: $\displaystyle P(1,\,e,\,\pi)$
    . . and the normal vector to the plane: .$\displaystyle \vec{n} \:=\:\langle1,\,e,\,\pi\rangle$

    The equation is: .$\displaystyle 1(x-1) + e(y-e) + \pi(z-\pi) \:=\:0\quad\Rightarrow\quad\boxed{\;x + ey - \pi z \:=\:e^2 + \pi^2 + 1\;}$

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  3. #3
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    I'm not sure why I didn't see that right away.
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