A) \[45{}^\circ \]
B) \[60{}^\circ \]
C) \[90{}^\circ \]
D) \[30{}^\circ \]
Correct Answer: D
Solution :
Here, \[\vec{a}\times (\vec{b}\times \vec{c})=\frac{1}{2}\vec{b}\] \[\Rightarrow \]\[(\vec{a}.\vec{c})\vec{b}-(\vec{a}.\vec{b})\vec{c}=\frac{1}{2}\vec{b}\] Since, \[\vec{b}\]and \[\vec{c}\]are non-parallel vectors. \[\therefore \]\[\vec{a}.\vec{c}=\frac{1}{2}\]and\[\vec{a}.\vec{b}=0\] Since \[\vec{a},\vec{b}\]and \[\vec{c}\]are unit vectors. \[\therefore \]\[\cos \beta =\frac{1}{2}\]and\[\cos \alpha =0\] \[\Rightarrow \]\[\beta ={{60}^{o}}\]and\[\alpha ={{90}^{o}}\] \[\therefore \]\[|\alpha -\beta |={{30}^{o}}\]
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