Point A | , | , | |
Point B | , | , | |
Point C | , | , |
Equation of the plane (given three points) | x+y+z+=0 |
There are three points A(x1, y1, z1), B(x2, y2, z2) and C(x3, y3, z3) lying on a plane, Then the plane equation can be found using the following formula
x - x1 | y - y1 | z - z1 | = 0 | ||
x2 - x1 | y2 - y1 | z2 - z1 | |||
x3 - x1 | y3 - y1 | z3 - z1 |
Or A(Ax,Ay,Az),B(Bx,By,Bz),C(Cx,Cy,Cz), the Equation of the plane is ax+by+cz+d=0
Where,
a = (By-Ay)(Cz-Az)-(Cy-Ay)(Bz-Az)
b = (Bz-Az)(Cx-Ax)-(Cz-Az)(Bx-Ax)
c = (Bx-Ax)(Cy-Ay)-(Cx-Ax)(By-Ay)
d = -(aAx+bAy+cAz).
Cartesian plane equation calculation with the three coordinates is made easier here.