Solveeit Logo
Login

Question

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

If x=ycos⁡2π3=zcos⁡4π3x = y\cos\frac{2\pi}{3} = z\cos\frac{4\pi}{3}, then xy+yz+zx=xy + yz + zx =

A

– 1

B

0

C

1

D

2

Answer

0

Explanation

Solution

We have x=ycos⁡2π3=zcos⁡4π3x = y\cos\frac{2\pi}{3} = z\cos\frac{4\pi}{3}

⇒x1=y−2=z−2=λ\Rightarrow \frac{x}{1} = \frac{y}{- 2} = \frac{z}{- 2} = \lambda (say)

⇒x=λ, 6muy=−2λ,z=−2λ\Rightarrow x = \lambda,\mspace{6mu} y = - 2\lambda,z = - 2\lambda

∴xy+yz+zx=−2λ2+4λ2−2λ2=0\therefore xy + yz + zx = - 2\lambda^{2} + 4\lambda^{2} - 2\lambda^{2} = 0.