## 1. Vector equation of a line through a point with p.v and parallel to any line.

2. Vector equation of a line through two points with p.v ‘s

3. The cartesian equation of a line with d.r’s and passing through a point.

4. The cartesian equation of a line passing through given two points.

5. Condition for three given points are collinear.

6. Three points A , B , C are collinear with p.v’s (a , b, c).

7. Area of a triangle :

(a). Cartesian Form :-

(b). Vector Form :-

8. Angle between two lines :

(a). Cartesian Form :-

(b). Vector Form :-

Note :-

(i). If two lines are perpendicular to each other then –

(ii). If two lines are parallel to each other then –

9. Perpendicular Distance of a Point from a line :-

(a). Cartesian Form :-

(b). Vector Form :-

10. Reflection or Image of a point in a straight line :

11. Shortest Distance between two Non – coplanar lines :-

(a). Vector Form :

(i). Shortest distance between two non – intersecting skew lines :

(ii). Distance between two parallel lines :

(b). Cartesian Form :

12. Condition for lines to Intersect :

(a). Vector Form :

(b). Cartesian Form :

13. Condition for two lines not Intersect :

14. Co-planar lines :

(a). Given two lines are Co – Planar :

(b). Given four lines are Co – Planar :

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