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  • Establish the following vector inequalities geometrically or otherwise: (d) |a - b| > | |a|- |b| |

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

(d)   \left | a-b \right |\geq \left | | a\right |-\left | b \right ||

Answers (1)

best_answer

Consider the image given below :

                                                      

In \DeltaOAB, we have :

                                                       OB +AB > OA

or                                                      OB > \left | OA - AB \right |

or                                                   \left | a-b \right |\ > \left | | a\right |-\left | b \right ||                               ...................................................(i)

Also, if the vectors are in a straight line then :

                                                       \left | a-b \right |\ = \left | | a\right |-\left | b \right ||                            .........................................................(ii)

From (i) and (ii), we can conclude :

                                                       \left | a-b \right |\geq \left | | a\right |-\left | b \right ||

Posted by

Devendra Khairwa

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