Cartesian Equation of the Plane Calculation
Calculate the equation of a three-dimensional plane in space for entered values.
Please enter the coordinates of :
Calculator find the equation of a three-dimensional plane in space, suppose the normal vector is defined as n = < A, B, C>
where :
n is a vector,
and A, B, and C are scalars.
n is a vector,
and A, B, and C are scalars.
We can determine the equation of the plane that contains the 3 point in the xyz-coordinate in following form:
ax + by + cz + d = 0
where a, b, c, and d are real numbers and derivation is as follows:
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).
Let's take the example where all the 3 points are as follows in three-dimensional space: