If x = y cos frac{2pi}{3} = z cos frac{4pi}{3 | vedclass

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(B) Given that $x = y \cos \frac{2\pi}{3} = z \cos \frac{4\pi}{3}$.We know that $\cos \frac{2\pi}{3} = -\frac{1}{2}$ and $\cos \frac{4\pi}{3} = -\frac

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(B) Given that $x = y \cos \frac{2\pi}{3} = z \cos \frac{4\pi}{3}$.We know that $\cos \frac{2\pi}{3} = -\frac{1}{2}$ and $\cos \frac{4\pi}{3} = -\frac{1}{2}$.So,$x = y(-\frac{1}{2}) = z(-\frac{1}{2})$.This implies $x = -\frac{y}{2} = -\frac{z}{2}$.Let $x = \lambda$,then $y = -2\lambda$ and $z = -2\lambda$.Now,calculate $xy + yz + zx$:$xy + yz + zx = (\lambda)(-2\lambda) + (-2\lambda)(-2\lambda) + (-2\lambda)(\lambda)$$= -2\lambda^2 + 4\lambda^2 - 2\lambda^2$$= 0$.

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

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