Question

The expression of $x+y+z=1$ in form of $x\cos \alpha +y\cos \beta +z\cos \gamma =p$ is _______.

• A. $x+y+z=1$
• B. $\frac{x}{2\sqrt{3}}+\frac{y}{2\sqrt{3}}+\frac{z}{2\sqrt{3}}=\frac{1}{\sqrt{3}}$
• C. $\frac{x}{\sqrt{3}}+\frac{y}{\sqrt{3}}+\frac{z}{\sqrt{3}}=1$
• D. $\frac{x}{\sqrt{3}}+\frac{y}{\sqrt{3}}+\frac{z}{\sqrt{3}}=\frac{1}{\sqrt{3}}$

Answer 1

The correct option is D $\frac{x}{\sqrt{3}}+\frac{y}{\sqrt{3}}+\frac{z}{\sqrt{3}}=\frac{1}{\sqrt{3}}$

$\frac{x}{\sqrt{3}}+\frac{y}{\sqrt{3}}+\frac{z}{\sqrt{3}}=1$
$\to P=\frac{|-1|}{\sqrt{1+1+1}}=\frac{1}{\sqrt{3}}$
$\therefore x+y+z=1$
$\therefore \frac{x}{\sqrt{3}}+\frac{y}{\sqrt{3}}+\frac{z}{\sqrt{3}}=\frac{1}{\sqrt{3}}$