Formula of (A vector + B vector).(A vector-B vector)
Formula of (A vector + B vector).(A vector-B vector)
Ramana , 6 Years ago
Grade 10
Vectors> Formula of (A vector + B vector).(A vecto...
3 Answers
Arun
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
Satwik Banchhor
Hey Ramana,
This problem can be solved using the following properties of dot product of vectors :-
- Distributive Property : A.(B+C) = A.B + A.C
- Commutative Property: A.B = B.A
- A.A = |A|2
(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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