6.8 Different forms of Equation of a plane

. Different forms of Equation of a plane We have already seen the notion of a plane. Definition . A vector 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. .

. Equation of a plane when a normal to the plane and the distance of