A) -1
B) 0
C) 1
D) 2
Correct Answer: B
Solution :
We have \[x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3}\] \[\Rightarrow \frac{x}{1}=\frac{y}{-2}=\frac{z}{-2}=\lambda \] (say) \[\Rightarrow x=\lambda ,\ y=-2\lambda ,\,z=-2\lambda \] \[\therefore xy+yz+zx=-2{{\lambda }^{2}}+4{{\lambda }^{2}}-2{{\lambda }^{2}}=0\].
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