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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  3-D Geometry
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The equation of the plane that meets the coordinated axis at the points $A,B,C$ respectively so that the centroid of the $\Delta ABC$ is $(\alpha,\beta,\gamma)$ is ?

$ (a)\: \alpha x+\beta y+\gamma z=1 \\(b)\: \large\frac{x}{\alpha}+\frac{y}{\beta}+\frac{z}{\gamma}=3 \\(c)\: \large\frac{x}{\alpha}+\frac{y}{\beta}+\frac{z}{\gamma}=1 \\ (d) \:\alpha x+\beta y+\gamma z=3 $

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Let the plane cut the coordinate axis at the points $A(a,0,0),\:B(0,b,0)\:and\:\:C(0,0,c)$
$\therefore$ The eqn. of the plane is $\large\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$
$\Rightarrow\:$Centroid of the $\Delta \:ABC$ is $\big(\large\frac{a}{3},\frac{b}{3},\frac{c}{3}\big)$
Given: centroid = $(\alpha,\beta,\gamma)$
$\therefore$ Eqn. of the plane is $\large\frac{x}{\alpha}+\frac{y}{\beta}+\frac{z}{\gamma}=3$
answered Jan 1, 2014 by rvidyagovindarajan_1
edited Sep 29, 2014 by sharmaaparna1

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