A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{6}\]
D) \[\frac{\pi }{2}\]
E) \[\frac{\pi }{12}\]
Correct Answer: C
Solution :
\[|\overrightarrow{a}|=1,|\overrightarrow{b}|=1,[\overrightarrow{a},\overrightarrow{b},\overrightarrow{a}\times \overrightarrow{b}]=\frac{1}{4}\] \[\Rightarrow \] \[(\overrightarrow{a}\times \overrightarrow{b}).(\overrightarrow{a}\times \overrightarrow{b})=\frac{1}{4}\] \[\Rightarrow \] \[{{(|\overrightarrow{a}||\overrightarrow{b}|\sin \theta )}^{2}}=\frac{1}{4}\Rightarrow {{\sin }^{2}}\theta =\frac{1}{4}\] \[\Rightarrow \] \[\sin \theta =\frac{1}{2}\] \[\Rightarrow \] \[\theta =\frac{\pi }{6}\]
You need to login to perform this action.
You will be redirected in
3 sec
