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  • Establish the following vector inequalities geometrically or otherwise: (a) |a + b| < |a| + |b|

Q. 4.6     Establish the following vector inequalities geometrically or otherwise :        

( a)  \left | a+b \right |\leq \left | a \right |+\left | b \right | 

Answers (1)

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Consider the image given below :-                                                        

                                            

In \DeltaOCB,     

                                              OB < OC+BC 

or                                            \left | a+b \right | < \left | a \right |+\left | b \right |                                                     ................................................(i)

But if         a\ and\ b are in a straight line then     |a+b|\ =\ |a|\ +\ |b|                 ...............................................(ii)

From (i) and (ii), we can conclude that,   

                                                   \left | a+b \right |\leq \left | a \right |+\left | b \right |

Posted by

Devendra Khairwa

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