A) \[\pi \]
B) \[\frac{\pi }{2}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{4}\]
Correct Answer: C
Solution :
\[\cos \theta =|{{l}_{1}}{{l}_{2}}+{{m}_{1}}{{m}_{2}}+{{n}_{1}}{{n}_{2}}|\] \[=\left| \frac{\sqrt{3}}{4}\times \frac{\sqrt{3}}{4}+\frac{1}{4}\times \frac{1}{4}+\frac{\sqrt{3}}{2}\times \left( \frac{-\sqrt{3}}{2} \right) \right|\] \[=\left| \frac{3}{16}+\frac{1}{16}-\frac{3}{4} \right|\] \[=\left| \frac{-2}{4} \right|=\frac{1}{2}\] \[\Rightarrow \] \[\theta =\frac{\pi }{3}\]
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