A plane meets the coordinate axes at points A- B- C and - - - is the centroid of the triangle ABC- Then the equation of the plane is

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Centroid of a Triangle

A plane meets...

Question

A plane meets the coordinate axes at points A, B, C and $(α, β, γ)$ is the centroid of the triangle ABC. Then the equation of the plane is

$\frac{x}{α} + \frac{y}{β} + \frac{z}{γ} = 3$

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$\frac{x}{α} + \frac{y}{β} + \frac{z}{γ} = 1$

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$\frac{3 x}{α} + \frac{3 y}{β} + \frac{3 z}{γ} = 1$

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$α x + β y + γ z = 1$

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Solution

The correct option is A
$\frac{x}{α} + \frac{y}{β} + \frac{z}{γ} = 3$

Let the co-ordinates of the points where the plane cuts the axes be (a,0,0), (0,b,0) and (0,0,c).
Since the centroid is $(α, β, γ)$ , we have $a = 3 α, b = 3 β, c = 3 γ$
The equation of the plane will be
$\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1 \Rightarrow \frac{x}{3 α} + \frac{y}{3 β} + \frac{z}{3 γ} = 1 \Rightarrow \frac{x}{α} + \frac{y}{β} + \frac{z}{γ} = 3$

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A plane meets the coordinate axes at points A, B, C and (α,β,γ) is the centroid of the triangle ABC. Then the equation of the plane is

The correct option is A xα+yβ+zγ=3 Let the co-ordinates of the points where the plane cuts the axes be (a,0,0), (0,b,0) and (0,0,c). Since the centroid is (α,β,γ), we have a= 3α,b= 3β,c= 3γ The equation of the plane will be xa+yb+zc=1⇒x3α+y3β+z3γ=1⇒xα+yβ+zγ=3

A plane meets the coordinate axes at points A, B, C and $(α, β, γ)$ is the centroid of the triangle ABC. Then the equation of the plane is