question_answer

If the vectors represented by the sides AB and BC of the regular hexagon ABCDEF be a and b, then the vector represented by \[\overrightarrow{AE}\] will be

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

B) \[\mathbf{b}-\mathbf{a}\]

C) \[2\,\mathbf{a}-\mathbf{b}\]              

D) \[\mathbf{a}+\mathbf{b}\]

Correct Answer: A

Solution :

As in figure \[\overrightarrow{AB}=\mathbf{a},\] \[\overrightarrow{BC}=\mathbf{b},\] so \[\overrightarrow{AD}=2\mathbf{b}\] and \[\overrightarrow{ED}=\mathbf{a}\]. Now, \[\overrightarrow{AE}+\overrightarrow{ED}=\overrightarrow{AD}\Rightarrow \overrightarrow{AE}=\overrightarrow{AD}-\overrightarrow{ED}=2\mathbf{b}-\mathbf{a}.\]