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