Find mod A vector+B vector maximum and mod A vector +B vector minimum also find A vector - B vector
Answers
What can be the maximum and minimum value of vectors a+b and a-b?
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In the present form the question is meaningless because it is not given about what is changing and what is not changing. If a and b are given fixed vector then the vectors a+b and a-b are also fixed and there is no question about maximum and minimum values of them. I guess what is meant that only the magnitudes |a| and |b| are fixed while their directions can change. Now |a+b|^2 =|a|^2 +|b|^2 +2|a|.|b|cos t which has minimum and maximum values according as cos t has minimum or maximum values i.e. 1 or (-1). Hence a+b has maximum modulus |a|+|b|, when the vectors point in the same direction and minimum modulus | |a|-|b| | when they point in opposite directions. As |b|=|-b|, the maximum and minimum values of moduli of a-b are also above, but they occur in opposite cases, i.e. the modulus of the difference is maximum when they point in opposite directions and it is minimum when they point in the same direction.