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Thread: planes

  1. #1
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    planes

    Hello,, how do you find 3 planes(p1,p2,p3) given a point of intersection (2,3,4,)? Thanks!
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    One elementary example is simply the $\displaystyle yz, xz, xy$ planes (they all intersect at the point $\displaystyle (0,0,0)$), and their respective equations are $\displaystyle x=0,y=0,z=0$.

    Three planes that intersect at any point $\displaystyle (a,b,c)$ are $\displaystyle x=a,y=b,x=c$. Three planes that intersect at $\displaystyle (2,3,4)$ are $\displaystyle x=2,y=3,z=4$.
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    Quote Originally Posted by Keep View Post
    Hello,, how do you find 3 planes(p1,p2,p3) given a point of intersection (2,3,4,)? Thanks!
    There exist an infinite number of planes passing through any given point. Given any point $\displaystyle (x_0,y_0,z_0)$, three planes that intersect there that are particularly easy are $\displaystyle x= x_0$, $\displaystyle y= y_0$, and $\displaystyle z= z_0$.
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  4. #4
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    And how does one get the implicit form (Hessian form) of the planes?
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