which is gr8r : |a+b| or |a|+|b|? (a , b are vectors ) give reasons ??

Asked by shuchi.saumya | 12th Sep, 2010, 12:00: AM

Expert Answer:

|a| + |b| is greater than |a+b|.
 
Reason: mod operator returns the positive value of the vector. Thus, |a| + |b| is sum of two positive quantities.
 
In |a+b|, the addition is done in the vectors before applying mod.
There can be three possibilities:
(i) Both the vecotrs positive
(ii) Both negative
(iii) one positive, one negative
 
(i) and (ii) return the same thing for |a + b| and |a| +|b|.
But for (iii), |a+b| implies a subtraction (since one of them is negative) first, and then mod of the result. this will be lesser than |a| + |b|, where first both the vectors will be turned positive and then ADDED.

Answered by  | 12th Sep, 2010, 09:09: PM

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