1. ## planes

Hello,, how do you find 3 planes(p1,p2,p3) given a point of intersection (2,3,4,)? Thanks!

2. 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 $x=2,y=3,z=4$.

3. 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 $z= z_0$.

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