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

|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.