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)

$0$

We have, $x=y\cos \frac{2\pi }{3}=z\cos \frac{4\pi }{3}$

$\Rightarrow x=\frac{-y}{2}=-\frac{z}{2}$

$\Rightarrow \frac{x}{1}=\frac{y}{-2}=\frac{z}{-2}=\lambda$ [say]

$\Rightarrow x=\lambda ,y=-2\lambda ,z=-2\lambda$

$\Rightarrow xy+yz+zx=-2{\lambda }^2+4{\lambda }^2-2{\lambda }^2=0$.