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

Question

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

Answer 1

We have $\frac{x}{1} = \frac{y}{- 2} = \frac{z}{- 2} = \lambda$ (say)

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

Question: If \(x = y\cos\frac{2\pi}{3} = z\cos\frac{4\pi}{3}\), then \(xy + yz + zx =\)...