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Three dimensional geometry
- 2. ο ο Direction Cosines and Direction Ratios of a Line ο Direction ratio also known as Direction Numbers ο Direction Cosine of a line are Direction Cosine of a Line
- 3. ο Direction Cosine of a Line Passing through two points
- 4. ο Direction Ratios of the line segment
- 5. ο Example
- 6. ο Example
- 7. ο A Line is uniquely determined if ο It passes through a given point and has given direction. ο It passes through two given points Equation of a Line in Space
- 8. ο 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. ο ο Cartesian equation of the line is Equation of a Line passing through a point Cartesian form
- 10. ο
- 11. ο Equation of a Line passing through two given points
- 12. ο
- 13. ο
- 14. ο Angle between two Lines
- 15. ο Example
- 16. ο ο If two lines in space intersect at a point, then the shortest distance between them is zero. ο If two lines in space are parallel, then the shortest distance between them will be the perpendicular distance. ο 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
- 17. ο ο The shortest distance between the skew lines l1 and With equations Shortest Distance between Skew Lines
- 18. ο Distance between the Parallel Lines
- 19. ο
- 20. ο
- 21. ο ο The vector form of the equation of the plane is In Cartesian Form Equation of a Plane in a Normal Form
- 22. ο
- 23. ο
- 24. ο Note
- 25. ο ο Cartesian form ο Vector form Equation of a plane perpendicular to a given vector and passing through a point
- 26. ο ο Vector Form ο Cartesian Form Equation of a plane passing through three non collinearpoints
- 27. ο
- 28. ο Intercept form of the equation of a plane
- 29. ο
- 30. ο ο Vector Form ο Cartesian Form Plane Passing through intersection of two planes
- 31. ο
- 32. ο Co planarity of two Lines
- 33. ο
- 34. ο
- 35. ο
- 36. ο
- 37. ο Distance of a point from a Plane
- 38. ο ο Vector form ο Cartesian form Distance of a point from a Plane
- 39. ο Angle between a line and a plane
- 40. ο