A) \[{{45}^{o}}\]
B) \[{{60}^{o}}\]
C) \[{{\cos }^{-1}}\left( \frac{1}{3} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{2}{7} \right)\]
Correct Answer: B
Solution :
\[(\mathbf{a}+2\mathbf{b})\,.\,(5\mathbf{a}-4\mathbf{b})=0\]or \[5{{\mathbf{a}}^{2}}+6\mathbf{a}\,.\,\mathbf{b}-8{{\mathbf{b}}^{2}}=0\] or \[6\,\mathbf{a}\,.\,\mathbf{b}=3,\] \[(\because {{\mathbf{a}}^{2}}=1,\,{{\mathbf{b}}^{2}}=1)\] \[\therefore \,\mathbf{a}\,.\,\mathbf{b}=\frac{1}{2}\] or \[|\mathbf{a}||\mathbf{b}|\,\,\cos \theta =\frac{1}{2}\] \[\therefore \,\cos \theta =\frac{1}{2}\,,\,\,\,\,\,\,\,\therefore \theta ={{60}^{o}}.\]
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