A) \[\pi /3\]
B) \[\pi /2\]
C) \[\pi /4\]
D) \[\pi /6\]
E) \[0\]
Correct Answer: A
Solution :
Given, projection of \[\vec{a}\] on \[\overrightarrow{b}=|\overrightarrow{a}\times \overrightarrow{b}|\] \[\Rightarrow \] \[\frac{\overrightarrow{a}\,.\,\overrightarrow{b}}{|\overrightarrow{b}|}=|\overrightarrow{a}\times \overrightarrow{b}|\] \[\Rightarrow \] \[\frac{|\overrightarrow{a}||\overrightarrow{b}|\cos \theta }{|\overrightarrow{b}|}=|\overrightarrow{a}||\overrightarrow{b}|\sin \theta \] \[\Rightarrow \] \[\tan \theta =\frac{1}{|\overrightarrow{b}|}\] \[\Rightarrow \] \[\tan \theta =\frac{1}{\frac{1}{3}\sqrt{{{1}^{2}}+{{1}^{2}}+{{1}^{2}}}}\] \[\Rightarrow \] \[\tan \theta =\sqrt{3}\] \[\Rightarrow \] \[\theta =\frac{\pi }{3}\]
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