A) \[\pm \frac{2}{15}\]
B) \[\frac{1}{5}\]
C) \[\pm \frac{1}{15}\]
D) None of these
Correct Answer: A
Solution :
\[{{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\] \[\Rightarrow \,\,\cos \,\gamma =\sqrt{1-{{\left( \frac{14}{15} \right)}^{2}}-{{\left( \frac{1}{3} \right)}^{2}}}\]\[=\sqrt{\frac{8}{9}-\left( \frac{196}{225} \right)}=\pm \frac{2}{15}\].
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