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Math Help - 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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  2. #2
    Senior Member Pinkk's Avatar
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    One elementary example is simply the yz, xz, xy planes (they all intersect at the point (0,0,0)), and their respective equations are x=0,y=0,z=0.

    Three planes that intersect at any point (a,b,c) are x=a,y=b,x=c. Three planes that intersect at (2,3,4) are x=2,y=3,z=4.
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  3. #3
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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 (x_0,y_0,z_0), three planes that intersect there that are particularly easy are x= x_0, y= y_0, and 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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