Fundamental Concepts

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(x₁ , y₁ , z₁ ) and Q (x₂ , y₂ , z₂ ) 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 = 90⁰ : 

21. If two lines are parallel to each other then θ = 0⁰ : 

 

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