planes

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March 23rd 2009, 03:04 PM
Keep

planes

Hello,, how do you find 3 planes(p1,p2,p3) given a point of intersection (2,3,4,)? Thanks!
March 23rd 2009, 03:22 PM
Pinkk

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 $x=2,y=3,z=4$ .
March 23rd 2009, 04:11 PM
HallsofIvy

Quote:

Originally Posted by Keep

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 $z= z_0$ .
March 25th 2009, 01:30 PM
Keep

And how does one get the implicit form (Hessian form) of the planes?

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