Question

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

• A. $0 , a d \theta$
• B. $a d \theta , 0$
• C. 0, 0
• D. None of these

Answer 1

Answer: (B)

$a d \theta , 0$

Answer 2

From the figure $| \overrightarrow { O B } | = a$

Also from triangle rule $\overrightarrow { O B } - \overrightarrow { O A } = \overrightarrow { A B } = \Delta \vec { a }$

$\Rightarrow | \Delta \vec { a } | = A B$

Using angle ⇒ AB = a . dθ

So $| \Delta \vec { a } | = a d \theta$

$\Delta a$ means change in magnitude of vector i.e. $| \overrightarrow { O B } | - | \overrightarrow { O A } |$ $\Rightarrow a - a = 0$

So $\Delta a = 0$