How do you solve a plane equation with 3 points?

I am have know clue how to solve a Plane equation. Its not making any sense to me! Please help me!!! Can you give a gooooood example and explain each step... Thank you!|||http://local.wasp.uwa.edu.au/~pbourke/ge鈥?/a>


shows two ways, although I'm going to explain something more closely related to the 2nd way.





(aside: I'm going to use Ax to mean "the x coordinate of point/vector A" in my notation, and explicitly write an asterisk when I want to do multiplication.)





Take three points, A, B, and C. Pick one of them to be the "middle", and find two vectors g and h from the middle to the other two points.


e.g. using A as the middle,


Gx=Ax-Bx


Gy=Ay-By


Gz=Az-Bz


and


Hx=Ax-Cx


Hy=Ay-Cy


Hz=Az-Cz


Then find the normal by computing the cross product of g and h:


http://en.wikipedia.org/wiki/Cross_produ鈥?/a>


links to


http://en.wikipedia.org/wiki/Rule_of_Sar鈥?/a>


if you need help computing that cross-product. The cross-product of g and h gets you a vector N that's normal to the plane.





Nx * X + Ny * Y + Nz * Z = k, a constant, gets you a series of planes that's parallel to the plane you need, depending on k. (X, Y, and Z are the coordinates in space)





Substiute the coordinates for one of your points (A, B, or C) into (X, Y, Z), and you'll have your k, aka "D"


e.g.


Nx * Ax + Ny * Ay + Nz * Az = k.


Subtract k from both sides, and you have


Nx * X + Ny * Y + Nz * Z - k = 0


which is your standard equation for a plane.





For another example, see


http://www.jtaylor1142001.net/calcjat/So鈥?/a>


who does this the same way I did.