Three dimensional geometry

All the basic concepts you need to know is presented in a very simple way for you to understand.

1. Three Dimensional Geometry

2. Direction Cosines and Direction Ratios of a Line Direction ratio also known as D irection Numbers Direction Cosine of a line are Direction Cosine of a Line

3. Direction Cosine of a Line Passing through two points

4. Direction Ratios of the line segment

5. Example

6. Example

7. A Line is uniquely determined if It passes through a given point and has given direction. It passes through two given points Equation of a Line in Space

8. Equation of a line through a given point and parallel to a given vector. Vector Equation of the line is given by Equation of a Line passing through a point Vector form

9. Cartesian equation of the line is Equation of a Line passing through a point Cartesian form

10. Equation of a Line passing through two given points

11. Angle between two Lines

12. Example

13. If two lines in space intersect at a point, then the shortest distance between them is zero. If two lines in space are parallel, then the shortest distance between them will be the perpendicular distance. In a space, there are lines which are neither intersecting nor parallel. Such a pair of lines are non coplanar and are called skew lines. Skew Lines

14. The shortest distance between the skew lines l1 and With equations Shortest Distance between Skew Lines

15. Distance between the Parallel Lines

16. The vector form of the equation of the plane is In Cartesian Form Equation of a Plane in a Normal Form

17. Note

18. Cartesian form Vector form Equation of a plane perpendicular to a given vector and passing through a point

19. Vector Form Cartesian Form Equation of a plane passing through three non collinearpoints

20. Intercept form of the equation of a plane

21. Vector Form Cartesian Form Plane Passing through intersection of two planes

22. Co planarity of two Lines

23. Distance of a point from a Plane

24. Vector form Cartesian form Distance of a point from a Plane

25. Angle between a line and a plane