Question

A plane meets the coordinate axes in $A,B,C$ and $(\alpha ,\beta ,\gamma )$ is centroid of the triangle $ABC$. Then the equation of the plane is

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

Answer 1

The correct option is A $\frac{x}{\alpha }+\frac{y}{\beta }+\frac{z}{\gamma }=3$

$A,B,C$ are points on axes, centroid is $(\alpha ,\beta ,\gamma )$

so coordinates of $A,B,C$ wil be $(\frac{3}{\alpha },0),(\frac{3}{\beta },0),(\frac{3}{\gamma },0)$

Now equation of plane will be $\frac{x}{3\alpha }+\frac{y}{3\beta }+\frac{z}{3\gamma }=1$

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