# planes

• Mar 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!
• Mar 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 $x=2,y=3,z=4$.
• Mar 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 $z= z_0$.
• Mar 25th 2009, 01:30 PM
Keep
And how does one get the implicit form (Hessian form) of the planes?