# planes

• Mar 23rd 2009, 02:04 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, 02:22 PM
Pinkk
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\$.
• Mar 23rd 2009, 03:11 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 \$\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\$.
• Mar 25th 2009, 12:30 PM
Keep
And how does one get the implicit form (Hessian form) of the planes?