Vector Algebra Question 376
Question: Let a and b be two unit vectors inclined at an angle $ \theta $ , then $ \sin ,(\theta /2) $ is equal to
[BIT Ranchi 1991; Karnataka CET 2000, 01; UPSEAT 2002]
Options:
A) $ \frac{1}{2}|a-b| $
B) $ \frac{1}{2}|a+b| $
C) $ |a-b| $
D) $ |a+b| $
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Answer:
Correct Answer: A
Solution:
- $ |\mathbf{a}-\mathbf{b}|=\sqrt{1^{2}+1^{2}-{{2.1}^{2}},\cos \theta }=\sqrt{2,(1-\cos \theta )} $ $ =\sqrt{2}\times \sqrt{2}\sin \frac{\theta }{2}=2\sin \frac{\theta }{2} $
$ \Rightarrow ,\sin \frac{\theta }{2}=\frac{|\mathbf{a}-\mathbf{b}|}{2} $ .
BETA
