question_answer 6)

Establish   the   following   vector   inequalities geometrically or otherwise: (a) (b) (c) (d)   When does the equality sign above apply ?  

Answer:

(a) If  be the angle between  and , then      Now  will be maximum when        Hence   The equality sign is applicable when  i.e., when  and  are in the same direction. (b) Again        The value of  will be minimum when   or            i.e.,     Hence The equality sign is applicable when  i.e., when  and  are in opposite directions. (c) If  is the angle between  and , then the angle between  and  will be  as shown in Fig. 4.100.     Fig. 4.100                  will be maximum when  or                Hence The equality sign is applicable when . (d)  will be minimum when  or     Hence The equality sign is applicable when .