Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class11  >>  3-D Geometry
0 votes

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 $

Can you answer this question?

1 Answer

0 votes
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

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App