A) \[\frac{1}{2}|a-b|\]
B) \[\frac{1}{2}|a+b|\]
C) \[|a-b|\]
D) \[|a+b|\]
Correct Answer: A
Solution :
\[|\mathbf{a}-\mathbf{b}|\text{ }=\sqrt{{{1}^{2}}+{{1}^{2}}-{{2.1}^{2}}\,\cos \theta }=\sqrt{2\,(1-\cos \theta )}\] \[=\sqrt{2}\times \sqrt{2}\sin \frac{\theta }{2}=2\sin \frac{\theta }{2}\] \[\Rightarrow \,\sin \frac{\theta }{2}=\frac{|\mathbf{a}-\mathbf{b}|}{2}\].
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