Vectors Question 218
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
Options:
A) $ 0,,a,d\theta $
B) $ a,,d\theta ,0 $
C) 0, 0
D) None of these
Correct Answer: D [d] $ |\Delta \vec{a}|=,\sqrt{a^{2}+,a^{2}-,2.a.a.\cos ,(d,\theta )} $
$ =2a\sin ,( \frac{d\theta }{2} ) $
For small angle
$ \sin ,\frac{d\theta }{2}\approx \frac{d\theta }{2} $ $ \ Therefore $ $ |\Delta \vec{a}|=2a,\times ,\frac{d\theta }{2}=,a.d\theta $
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BETA
