question_answer

A vector \[\overrightarrow{a}\] is turned without a change in its length through a small angle \[d\theta .\]The value of \[|\Delta \overrightarrow{a}|\] and \[\Delta a\] are respectively

A)             \[0,\,a\,d\theta \]

B)                                         \[a\,d\theta ,\,0\,\]

C)             0, 0

D)             None of these

Correct Answer: B

Solution :

                From the figure \[|\overrightarrow{OA}|\,=a\] and \[|\overrightarrow{OB}|\,=a\]                    Also from triangle rule \[\overrightarrow{OB}-\overrightarrow{OA}=\overrightarrow{AB}=\Delta \overrightarrow{a\,}\] \[\Rightarrow \,\,\,|\Delta \overrightarrow{a\,}|\,=AB\]                    Using angle \[=\frac{\text{arc}}{\text{radius}}\]                     Þ  AB = a . dq                    So \[|\Delta \overrightarrow{a\,}|\,=\,a\,d\theta \]                    \[\Delta a\] means change in magnitude of vector i.e. \[|\overrightarrow{OB}|-|\overrightarrow{OA}|\] \[\Rightarrow \,\,\,a-a=0\]             So \[\Delta a=0\]