Different forms of Equation of a plane

Different forms of Equation of a plane

We have already seen the notion of a plane.

Definition 6.8

A straight line which is perpendicular to a plane is called a normal to the plane.

Note

Every normal to a plane is perpendicular to every straight line lying on the plane.

A plane is uniquely fixed if any one of the following is given:

·            a unit normal to the plane and the distance of the plane from the origin

·            a point of the plane and a normal to the plane

·            three non-collinear points of the plane

·            a point of the plane and two non-parallel lines or non-parallel vectors which are parallel to the plane

·            two distinct points of the plane and a straight line or non-zero vector parallel to the plane but not parallel to the line joining the two points.

Let us find the vector and Cartesian equations of planes using the above situations.