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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