A) \[30{}^\circ \]
B) \[90{}^\circ \]
C) \[60{}^\circ \]
D) \[45{}^\circ \]
Correct Answer: A
Solution :
\[(\vec{a}.\vec{c})\vec{b}-\left( \vec{a}\vec{b} \right).\vec{c}=\frac{1}{2}\vec{b}\] |
\[\because \]\[\vec{b}\] and \[\vec{c}\] are linearly independent |
\[\because \]\[\vec{a}.\vec{c}=\frac{1}{2}\] and \[\overrightarrow{a}.\overrightarrow{b}=0\] |
(All given vectors are unit vectors) |
\[\because \]\[\vec{a}\wedge \vec{c}=60{}^\circ \]and \[\vec{a}\wedge \vec{b}=90{}^\circ \] |
\[\because \] \[\left| a-\beta \right|=30{}^\circ .\] |
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