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KEAM 2010 Math Paper

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Question : 12 of 120

Marks: +1, -0

A plane makes intercepts

a, b,

A, B, C

on the coordinate axes respectively. If the centroid of the

\triangle A B C

(3,2,1),

then the equation of the plane is

$x+2y+3z=9$
$2x-3y-6z=18$
$2x+3y+6z=18$
$2x+y+6z=18$
$2x+3y+6z=9$

Solution:

Coordinates of

A, B

and

C

are

(a, 0,0),(0, b, 0)

and

(0,0, c)

respectively since, centroid of

\triangle A B C

is (3,2,1)

\therefore\; \frac{a+0+0}{3}=3

\Rightarrow\; a=9

and

\; \frac{0+b+0}{3}=2

\Rightarrow\; b=6

and

\frac{0+0+c}{3}=1

\Rightarrow\; c=3

∴ Equation of required plane is

\; \frac{x}{a}+\; \frac{y}{b}+\; \frac{z}{c}=1

\Rightarrow\; \frac{x}{9}+\; \frac{y}{6}+\; \frac{z}{3}=1

\Rightarrow\; 2x+3y+6z=18

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