A) \[1\]
B) \[0\]
C) \[-1\]
D) None of these
Correct Answer: B
Solution :
We have \[\frac{x}{\cos \theta }=\frac{y}{\cos \left( \theta -\frac{2\pi }{3} \right)}=\frac{z}{\cos \left( \theta +\frac{2\pi }{3} \right)}=k\] Þ \[x=k\cos \theta \], \[y=k\cos \left( \theta -\frac{2\pi }{3} \right)\], \[z=k\cos \left( \theta +\frac{2\pi }{3} \right)\] Þ \[x+y+z=k\left[ \cos \theta +\cos \left( \theta -\frac{2\pi }{3} \right)+\cos \left( \theta +\frac{2\pi }{3} \right) \right]\] \[=k[(0)=0\] \[\Rightarrow \] \[x+y+z=0\].
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