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 agoA plane meets the coordinate axes in points A, B, C and the centroid of the triangle ABC is (1, -2, 3). Find the equation of the plane.

Write the equation of the plane whose intercepts on the coordinate axes are \( \dfrac{x}{a}+ \dfrac{y}{b}+ \dfrac{z}{c}=1\)

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