question_answer

If a and b are the vectors determined by two adjacent sides of regular hexagon, then vector EO is

A) \[(a+b)\]           

B)        \[(a-b)\]              

C)         2 a                        

D)         2b

Correct Answer: B

Solution :

\[\text{OABCDE}\]is a regular hexagon. Let \[\overline{\text{OA}}=\bar{a}\]and \[AB=b,\]join OB OC, we have \[OB=OA+AB=a+b\]                 Since, OC is parallel to AB and double of AB.                 \[\therefore \]  \[OC=2\,AB=2b\]                 Now,     \[BC=OC-OB\]                                 \[=2b-(a+b)=b-a\]                                 \[CD=-OA=-a\]                 and        \[DE=-AB=-b\]                 Also,      \[EO=BC=-(b-a)=a-b\]