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

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

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

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Consider the image given below:-   

                                              

In \DeltaOAB,  we have

                                                        OB < OA+AB

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

For vectors in a straight line,           \left | a-b \right |\ =\ \left | a \right |+\left | b \right |                              ...........................................................(ii)

From (i) and (ii) we get  :

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

Posted by

Devendra Khairwa

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