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

Asked by Aaryan | 1 year ago |  168

##### Solution :-

Given:

The plane meets axes in A, B and C.

Let A = (a, 0, 0), B = (0, b, 0) and C = (0, 0, c)

Given that the centroid of the triangle = (α, β, γ)

By using the formula,

$$(α, β, γ)=(\dfrac{a}{3}, \dfrac{b}{3}, \dfrac{c}{3})$$

So,

$$\dfrac{a}{3}$$ = α

= a = 3α …… (i)

$$\dfrac{b}{3}$$ = β

= b = 3β ……. (2)

$$\dfrac{c}{3}$$ = γ

= c = 3γ ……. (3)

If a, b, c is intercepts by plane on coordinate axes,

Then equation of plane is given by:

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

Hence, the equation of plane is

$$\dfrac{x}{\alpha}+ \dfrac{y}{\beta}+ \dfrac{z}{\gamma}=1$$

Answered by Sakshi | 1 year ago

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