A vector vec A is rotated by a small angle Delta θ radian ( Delta θ << 1) to get a new vecto

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3-1.Vectors

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A vector $\vec A $ is rotated by a small angle $\Delta \theta$ radian $( \Delta \theta << 1)$ to get a new vector $\vec B$ In that case $\left| {\vec B - \vec A} \right|$ is

A

$\left| {\vec A} \right|\,\Delta \theta $

B

$\left| {\vec B} \right|\,\Delta \theta - \left| {\vec A} \right|\,$

C

$\left| {\vec A} \right|\,\left( {1 - \frac{{\Delta {\theta ^2}}}{2}} \right)$

D

$0$

(JEE MAIN-2015)

Solution

$\begin{array}{l}
Arc\,length\, = \,radius \times angle\\
So,\,\left| {\vec B – \vec A} \right| = \left| {\vec A} \right|\Delta \theta
\end{array}$

Standard 11

Physics

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