Page 3 - XII-CH10-VECTOR-LESSON NOTES

 
  |a  b|
19. Area of a triangle whose two sides are represented by a and b is given by .
2

20. Cosine formulae: If a, b, c are lengths of the opposite sides respectively to the angles A, B and C
of a triangle ABC, then
b  2 c  2 a 2 c  2 a  2 b 2 a  2 b  2 c 2
(i) cosA  (ii) cosB  (iii) cosC 
2bc 2ac 2ab
21. Projection formulae: If a, b, c are lengths of the opposite side respectively to the angles A, B
and C of a triangle ABC, then






(i) a bcosC ccosB (ii) b ccosA acosC (iii) c acosB bcosA
 
22. For any two vectors a and b , we have
     
2

2


2
(i) |a b| |a|  |b| 2|a||b|
     

2
2


2
(ii) |a b| |a|  |b| 2|a||b|
     
(iii) |a b|  |a b| 2[|a|  |b| ]

2
2
2


2
     

2

(iv) (a b).(a b) |a| 2 |b|

Reference Books:-
Mathematics part – 2: R.D.Sharma.
Mathematics part – 2: Pradeep publication.
Mathematics part -2: R.S. Aggarwal