question_answer

In a regular hexagon ABCDEF, \[\overrightarrow{AE}=\]                                                                              [MNR 1984]

A)                 \[2\mathbf{a}-3\mathbf{b}\]              

B)                 \[\overrightarrow{AC}\,\,+\,\,\overrightarrow{AF}\,\,-\,\overrightarrow{AB}\]

C) \[\overrightarrow{AC}\,\,+\,\,\overrightarrow{AB}\,\,-\,\,\overrightarrow{AF}\]           

D) None of these

Correct Answer: B

Solution :

Obviously, \[\overrightarrow{AE}=\overrightarrow{AC}+\overrightarrow{CD}+\overrightarrow{DE}\] \[=\overrightarrow{AC}+\overrightarrow{AF}-\overrightarrow{AB}\],  \[\left\{ \,\because \,\,\overrightarrow{CD}=\overrightarrow{AF}\,\text{and}\,\overrightarrow{DE}=-\overrightarrow{AB} \right\}\].