General Equation of a Plane from Normal and Point

General Equation of a Plane from Normal and Point

For normal vector:

$$\vec n=A\hat i+B\hat j+C\hat k$$

and point:

$$P(x_1,y_1,z_1)$$

the plane is:

$$A(x-x_1)+B(y-y_1)+C(z-z_1)=0$$

Usage

- Used as the quickest method to construct a plane from a point and normal.

For normal vector:

$$\vec n=A\hat i+B\hat j+C\hat k$$

and point:

$$P(x_1,y_1,z_1)$$

the plane is:

$$A(x-x_1)+B(y-y_1)+C(z-z_1)=0$$

Usage

- Used as the quickest method to construct a plane from a point and normal.