Question

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

• A. $0,adtheta$
• B. $adtheta,0$
• C. $0,0$
• D. $Noneofthese$

Answer 1

The correct option is B $adtheta,0$

From figure $\left|\overrightarrow{OA}\right|=a$ and $\left|\overrightarrow{OB}\right|=a$

Also from $\Delta$ rule

$\overrightarrow{OB}-\overrightarrow{OA}=\overrightarrow{AB}=\Delta \overrightarrow{a}\Rightarrow \left|\Delta \overrightarrow{a}\right|=AB$

$angle=\frac{arc}{radian}\Rightarrow AB=a.dq\left|\Delta \overrightarrow{a}\right|=ad\theta$

$\Delta a$ means change in magnitude of vector i.e,

$\left|\overrightarrow{OB}\right|-\left|\overrightarrow{OA}\right|\Rightarrow a-a=0\Delta a=0$