Question

If $x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3},$ then $xy+yz+zx$ is equal to

• A. -1
• B. 0
• C. 1
• D. 2

Answer 1

Answer: (B)

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] $\Rightarrow$ $x=\lambda ,y=-2\lambda ,z=-2\lambda$ $\Rightarrow$ $xy+yz+zx=-2{\lambda }^2+4{\lambda }^2-2{\lambda }^2=0$