The Plane

1. General equation of a Plane in the cartesian form :-

2. Equation of a Plane passing through a given Point :

3. Equation of a Plane in the intercept Form :

4. Equation of a Plane in the Normal form :

Vector Form : –

Cartesian Form :

5. Equation of a Plane parallel to a given Plane.

Vector Form :

Cartesian Form :

6. Equation of a Plane through the Intersection of two Plane :

Vector Form :

Cartesian Form :

7. Equation of a Plane passing through a given Point and perpendicular to a given vector.

Vector Form :

Cartesian Form :

8. Equation of a plane passing through a given point and parallel to two given lines.

Vector Form :

Parametric Form :

Cartesian Form :

9. Equation of Plane passing through three given points.

Vector Form :

Cartesian Form :

10. Angle between two Planes :

Vector Form :

Note : –

(i). If given two planes perpendicular to each other.

(ii). If given two planes parallel to each other.

Cartesian Form :

Note : –

(i). If given two planes perpendicular to each other.

(ii). If given two planes parallel to each other.

Important Point :

11. Angle between a line and Plane.

Vector Form :

Note Points : If given line and Plane perpendicular and parallel to each other.

Cartesian Form :

Note Points : If given line and Plane perpendicular and parallel to each other.

12. Length of Perpendicular form a point to a Plane :

Vector Form :

Cartesian Form :

13. Condition for the Coplanarity of two lines.

Vector Form :

Note :-

Cartesian Form :

Note : –

The Plane