A plane meets the co-ordinates axes in A- B- C and - - Y is the centroid of the - ABC- Then the equation of the plane is-A- 3 x-3 y-3 z-y-1B- - x- y-y z-1C- x-y-z-1D- x-y-z-3

The correct option is D x/α+y/β+z/γ=3Let equation of plane be x/a+y/b+z/c=1 Then A = (a, 0, 0), B = (0, b, 0), C = (0, 0, c) Centroid of the Δ ABC =(a/3,b/3,c/ ...

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Byju's Answer

Standard XII

Mathematics

Equation of a Plane Passing through Three Points

A plane meets...

Question

A plane meets the co-ordinates axes in A, B, C and $(α, β, γ)$ is the centroid of the $Δ A B C$ . 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 equation of plane be $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$
Then A = (a, 0, 0), B = (0, b, 0), C = (0, 0, c)
Centroid of the $Δ A B C = (\frac{a}{3}, \frac{b}{3}, \frac{c}{3}) = (α, β, γ)$
$∴ a = 3 α, b = 3 β, c = 3 γ$
Hence, equation of the plane is $\frac{x}{α} + \frac{y}{β} + \frac{z}{γ} = 3$

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A plane meets the co-ordinates axes in A, B, C and (α,β,γ) is the centroid of the ΔABC. Then the equation of the plane is :

The correct option is A xα+yβ+zγ=3Let equation of plane be xa+yb+zc=1 Then A = (a, 0, 0), B = (0, b, 0), C = (0, 0, c) Centroid of the ΔABC=(a3,b3,c3)=(α,β,γ) ∴a=3α,b=3β,c=3γ Hence, equation of the plane is xα+yβ+zγ=3

A plane meets the co-ordinates axes in A, B, C and $(α, β, γ)$ is the centroid of the $Δ A B C$ . Then the equation of the plane is :