Question

The equation of the plane, which makes with co-ordinate axes a triangle with its centroid (α, β, γ), is

• A. $\alpha x + \beta y + \gamma z = 3$
• B. $\frac { x } { \alpha } + \frac { y } { \beta } + \frac { z } { \gamma } = 1$
• C. $\alpha x + \beta y + \gamma z = 1$
• D. $\frac { x } { \alpha } + \frac { y } { \beta } + \frac { z } { \gamma } = 3$

Answer 1

Answer: (D)

$\frac { x } { \alpha } + \frac { y } { \beta } + \frac { z } { \gamma } = 3$

Answer 2

We know that $\frac { x } { a } + \frac { y } { b } + \frac { z } { c } = 1$ ……(i)

Centroid $\left( \frac { a } { 3 } , \frac { b } { 3 } , \frac { c } { 3 } \right)$ i.e. $\alpha = a / 3 , \beta = b / 3 , \gamma = c / 3$

⇒ $a = 3 \alpha , b = 3 \beta , c = 3 \gamma$

From equation (i), $\frac { x } { 3 \alpha } + \frac { y } { 3 \beta } + \frac { z } { 3 \gamma } = 1$

∴ $\frac { x } { \alpha } + \frac { y } { \beta } + \frac { z } { \gamma } = 3$ .