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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
$0,\,a\,d\theta $
$a\,d\theta ,\,0\,$
$0, 0$
None of these
Solution
(b) 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{{{\rm{arc}}}}{{{\rm{radius}}}}$
$⇒ AB = a . d \theta$
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 $\Delta a = 0$
