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

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

(b)  |a+b|\geq |\; |a|-| b|\; |

Answers (1)

best_answer

Consider the given image: 

                        

In \DeltaOCB, we have:

Sum of two sides of a triangle is greater than the length of another side.

or                                                          OB+BC > OC

or                                                                OB > \left | OC - BC \right |

or                                                               |a+b|\ >\ |\; |a|-| b|\; |                         ............................................................(i)

Also,  if a\ and\ b are in a straight line but in the opposite direction then 

                                                                  |a+b|\ =\ |\; |a|-| b|\; |                           ...............................................................(ii)

From (i) and (ii), we get  :

                                                                   |a+b|\geq |\; |a|-| b|\; |

Posted by

Devendra Khairwa

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