Question

If a plane meets the coordinate axes at $\text{A, B}$ and $C$ such that the centroid of the triangle is $\text{(1, 2, 4),}$ then the equation of the plane is

• A. $\text{x + 2y + 4z = 12}$
• B. $\text{4x + 2y + z = 12}$
• C. $\text{x + 2y + 4z = 3}$
• D. $\text{4x + 2y + z = 3}$

Answer 1

The correct option is B

$\text{4x + 2y + z = 12}$

Explanation for the correct option:

Finding the equation of the plane:

Given,

Centroid of the triangle $=\left(1,2,4\right)$

Assume three points on the co-ordinate axes are $\text{A =}\left(a,0,0\right),B=\left(0,b,0\right)andC=\left(0,0,c\right)$

Therefore, $\frac{a}{3}=1\Rightarrow a=3$

$\frac{b}{3}=2\Rightarrow b=6$

$\frac{\text{c}}{3}=4\Rightarrow c=12$

we know that, equation of the plane is

$\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$

$\frac{x}{3}+\frac{y}{6}+\frac{z}{12}=1$

$\mathbf{\text{∴ 4x + 2y +z = 12}}$

Hence, option $\mathbf{\text{"B"}}$ is correct.