## 1. Three – Dimensional Co – ordinate System :

2. Origin :

3. Position Vector of a Point :

4. Sign of co – ordinate Point :

5. Two dimensional Geometry :

6. Three dimensional Geometry :

7. Co – ordinate of a Point P on axis :

8. Co – ordinates of a point in xy , yz and zx – Planes :

9. Equation of xy , yz and zx – planes :

10. Projection of the line segment joining two points on a line :

11. Projection of a point on a line :

12. Distance Formula :

(a). Distance b/w origin O(0, 0, 0) and any point P(x , y , z) :

(b). Distance of a point P from co – ordinate axis :

(c). Distance between the points P(x_{1} , y_{1} , z_{1} ) and Q (x_{2} , y_{2} , z_{2} ) is

13. Section Formula :

For internal dividing of given two points :-

For externally dividing of given two points :-

For midpoint of given two points :-

14. Centroid of a Triangle :

15. Incentre of Triangle :

16. Division by co – ordinate plane :

17. Direction Ratios :

18. Direction Cosines :

19. Angle Between two lines :

Cartesian Form :-

Vector Form :-

20. If two lines are perpendicular to each other then θ = 90^{0} :

21. If two lines are parallel to each other then θ = 0^{0} :

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