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Formula of (A vector + B vector).(A vector-B vector)

Formula of (A vector + B vector).(A vector-B vector)

Grade:10

3 Answers

Arun
25758 Points
2 years ago
Dear student
 
This is simply dot product.
 
it can be expanded as
 
A.A -A.B + B.A – B.B = B.A – A.B
 
Hope it helps
 
Regards
Arun
Saurabh Koranglekar
askIITians Faculty 10336 Points
2 years ago
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Satwik Banchhor
32 Points
2 years ago
Hey Ramana,
This problem can be solved using the following properties of dot product of vectors :-
  1. Distributive Property : A.(B+C) = A.B + A.C
  2. Commutative Property: A.B = B.A
  3. A.A = |A|
(A + B) . (A – B) 
= A . (A – B) + B . (A – B)    Using Distributive Property
= A.A – A.B + B.A – B.B      Using Distributive Property
= A.A  – B.B                         As A.B = B.A by Commutative Property
= |A|2 – |B|2
  

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