# Plane equation given three points Calculator

## Calculates the plane equation given three points.

 Point A ( , , )
 Point B ( , , )
 Point C ( , , )

 Plane equation: ax+by+cz+d=0

 x + y + z + =0
 $\normal Plane\ equation\hspace{20}{\large ax+by+cz+d=0}\\\vspace{5}(1)\ \vec{AB}=(B_x-A_x,B_y-A_y,B_z-A_z)\\\hspace{25} \vec{AC}=(C_x-A_x,C_y-A_y,C_z-A_z)\\\vspace{5}(2)\ \vec{AB}\times \vec{AC}=(a,b,c)\\\hspace{10} a=(B_y-A_y)(C_z-A_z)-(C_y-A_y)(B_z-A_z)\\\hspace{10} b=(B_z-A_z)(C_x-A_x)-(C_z-A_z)(B_x-A_x)\\\hspace{10} c=(B_x-A_x)(C_y-A_y)-(C_x-A_x)(B_y-A_y)\\\hspace{10} d=-(aA_x+bA_y+cA_z)\\$

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