A) \[\frac{1}{2}\,\left| \,{{{\vec{e}}}_{1}} \right.+\left. {{{\vec{e}}}_{2}} \right|\]
B) \[\frac{1}{2}\,\left| \,{{{\vec{e}}}_{1}} \right.-\left. {{{\vec{e}}}_{2}} \right|\]
C) \[\frac{{{{\vec{e}}}_{1}}\,\,.\,\,{{{\vec{e}}}_{2}}}{2}\]
D) \[\frac{\left| \,{{{\vec{e}}}_{1}} \right.\times \left. {{{\vec{e}}}_{2}} \right|}{2\left| \,{{{\vec{e}}}_{1}} \right|\,\,\left| {{{\vec{e}}}_{2}} \right|}\]
Correct Answer: B
Solution :
Consider \[{{\left| {{{\hat{e}}}_{1}}-{{{\hat{e}}}_{2}} \right|}^{2}}=2-2\,\,\cos \theta =4{{\sin }^{2}}\frac{\theta }{2}\] \[\therefore \,\,\frac{1}{2}{{\left| {{{\hat{e}}}_{1}}-{{{\hat{e}}}_{2}} \right|}^{2}}=\sin \frac{\theta }{2}\]
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