A) 1
B) 0
C) 2
D) \[3\cos \theta \]
Correct Answer: B
Solution :
Given that, \[x\cos \theta =y\cos \left( \theta +\frac{2\pi }{3} \right)=z\cos \left( \theta +\frac{4\pi }{3} \right)=k\](say) \[\Rightarrow \]\[\cos \theta =\frac{k}{x},\cos \left( \theta +\frac{2\pi }{3} \right)=\frac{k}{y}\] and\[\cos \left( \theta +\frac{4\pi }{3} \right)=\frac{k}{y}\] Now, \[\frac{k}{x}+\frac{k}{y}+\frac{k}{z}=\cos \theta +\cos \left( \theta +\frac{2\pi }{3} \right)\]\[+\cos \left( \theta +\frac{4\pi }{3} \right)\] \[=\cos \theta -\cos \left( \frac{\pi }{3}-\theta \right)-\cos \left( \frac{\pi }{3}+\theta \right)\] \[=\cos \theta -2\cos \frac{\pi }{3}\cos \theta =0\] \[\Rightarrow \]\[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0\]
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