504
edits
Changes
→How to find the equation of a plane from three points
First, you must find the vector normal to the plane. This is found by calculating the [[cross product]] of two vectors in the plane.
First, you must find the vector normal to the plane. This is found by calculating the [[cross product]] of two vectors in the plane.
vector AB = <(x<sub>B</sub> - x<sub>A</sub>), (y<sub>B</sub> - y<sub>A</sub>), (z<sub>B</sub> - z<sub>A</sub>)>
<br>vector AB = <(x<sub>B</sub> - x<sub>A</sub>), (y<sub>B</sub> - y<sub>A</sub>), (z<sub>B</sub> - z<sub>A</sub>)>
vector BC = <(x<sub>C</sub> - x<sub>B</sub>), (y<sub>C</sub> - y<sub>B</sub>), (z<sub>C</sub> - z<sub>B</sub>)>
<br>vector BC = <(x<sub>C</sub> - x<sub>B</sub>), (y<sub>C</sub> - y<sub>B</sub>), (z<sub>C</sub> - z<sub>B</sub>)>
AB cross BC = <D, E, F>
<br>AB cross BC = <D, E, F>
(D, E, and F stand for the numbers found when the cross product is calculated.)
<br>(D, E, and F stand for the numbers found when the cross product is calculated.)
<br><br>
The equation of the plane is then D(x - x<sub>A</sub>) + E(y - y<sub>A</sub>) + F(z - z<sub>A</sub>) = 0
The equation of the plane is then D(x - x<sub>A</sub>) + E(y - y<sub>A</sub>) + F(z - z<sub>A</sub>) = 0
(The coordinates of points B and C could have been used instead.)
<br>(The coordinates of points B and C could have been used instead.)
<br>
[[Category:Geometry]]
[[Category:Geometry]]