4.0 Plane

4.1 Equation of plane in normal form
4.2 Equation of a plane perpendicular to a given vector and passing through a given point
4.3 Equation of plane passing through a given point and parallel to the two given vectors
4.4 Equation of plane passing through three non-collinear points
4.5 Intercept form of plane
4.6 Equation of plane passing through the intersection of two given planes

A plane is a surface on which if any two points are taken,

1. The line segment joining them lies completely on the surface.

2. the line segment joining them is perpendicular to some fixed straight line. The fixed line is called normal to the plane.

An equation of a plane can be determined if the following three conditions are given:

1. the distance of plane from origin and a normal vector to the plane (normal form).

2. a point through which the plane passes and normal vector to the plane.

3. three non collinear points through which plane passes.

Note: If any other condition is given, then we have to use the given conditions in such a way to find any one of the conditions mentioned above and find the equation of plane.