Question

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

• A. $0,ad\theta$
• B. $ad\theta ,\theta$
• C. $0,0$
• D. $ad\theta ,ad\theta$

Answer 1

The correct option is A $0,ad\theta$

Given, $Angle=d\theta ,\overrightarrow{a}$4

We have a $\overrightarrow{a}$ is draw $\overrightarrow{AB}=|\overrightarrow{AB}|=a$

Now, This vector is turned through an angle, then using the triangle law:

$\Delta \overrightarrow{a}=\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}=\overrightarrow{OB}+(-\overrightarrow{OA})$

Angle between \vec {OB} and -\vec {OA}180^0-d\theta=|\Delta \vec a|=\Delta a$

$(\Delta a{)}^2=a^2+a^{2}2a^{2}cos(180-d\theta )=2a^2[1-1+2s{i}^{2}sin\frac{d\theta }{2}]=4a^{2}si{n}^2\frac{d\theta }{2}$