A) \[2\sin \left( \frac{\theta }{2} \right)\]
B) \[2\cos \left( \frac{\theta }{2} \right)\]
C) \[\sin \left( \frac{\theta }{2} \right)\]
D) \[\cos \left( \frac{\theta }{2} \right)\]
E) \[\left( \frac{\theta }{2} \right)\]
Correct Answer: A
Solution :
\[|\overrightarrow{x}-\overrightarrow{y}{{|}^{2}}={{\overrightarrow{x}}^{2}}+{{\overrightarrow{y}}^{2}}-2\overrightarrow{x}.\overrightarrow{y}\] \[=1+1-2\cos \theta \] \[=2(1-\cos \theta )=2.2{{\sin }^{2}}\left( \frac{\theta }{2} \right)\] \[\Rightarrow \] \[|\overrightarrow{x}-\overrightarrow{y}{{|}^{2}}=4{{\sin }^{2}}\left( \frac{\theta }{2} \right)\] \[\Rightarrow \] \[|\overrightarrow{x}-\overrightarrow{y}|=2\sin \left( \frac{\theta }{2} \right)\]
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