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If a and b are unit vectors then the greatest value of |a+b| and |a-b| is?

If a and b are unit vectors then the greatest value of |a+b| and |a-b| is?

Grade:12th Pass

2 Answers

Vikas TU
14149 Points
one year ago
Dear student 
a, b are unit vector , then the greatest value of |a+b| 
Will be equal to sqrt (1+1 = 1.414
Minimum value would be – 1.414
Hope this helps
Good luck 
Satwik Banchhor
32 Points
one year ago
Hey Sridev,
To solve this problem we can use the following property :-
|A|2 = A . A
and 
A.B = |A||B| cos(θ) where θ is the angle between the vectors A and B
 
Given A and B are unit vectors:- 
A.A = B.B = 1
 
|A + B|2
=  (A + B) . (A + B) 
=  A.A + 2A.B +B.B
= 2(1 + |A|*|B|*cos(θ) )
= 2(1 + cos(θ))
which attains its maximum value when cos(θ) = 1. This is the case when the two vectors are in the same direction.
Therefore maximum value of |A+B|2 is 4.
Therefore maximum value of |A+B| is 2.
 
Similarly for |A-B| you can show that the magnitude attains a maximum value of 2 when A and B are opposite to each other i.e. cos(θ) = -1.
 
 

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