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What can be the maximum value of magnitude of ( a vector - B vector)

What can be the maximum value of magnitude of ( a vector - B vector) 

Grade:11

2 Answers

Arun
25757 Points
3 years ago
Dear student
 
Question is incomplete. Please check and repost the complete Question. You can also attach an image. I will be happy to help you.
 
Regards
Arun
Satwik Banchhor
32 Points
3 years ago
Hey Debapriya,
The problem can be solved as follows:
|A - B|2
= (A – B) . (A – B)
= A.A – 2A.B + B.B
= |A|2 – 2 |A|*|B|*cos(θ) + |B|2
which attains its maximum value when cosθ = -1 therefore,
max( |A – B|2 ) = |A|2 + 2 |A|*|B| + |B|2 = (|A| + |B|)2
Therefore,
max ( |A – B| ) = |A| + |B| , when cosθ = -1.
 
Note: When cosθ = -1 then the two vectors point in opposite directions and that is when |A – B| attains its maximum value.

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