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Question

The plane ax+by+cz=1 meets the coordinates axes at A, B and C. The centroid of ABC is


A

(3a,3b,3c)

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B

a3,b3,c3

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C

13a,13b,13c

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D

(a,b,c)

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Solution

The correct option is C

13a,13b,13c


Find the coordinates of the centroid

The plane ax+by+cz=1 meets the coordinate axis in A,B,C, then the coordinates will be,

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

The equation of the plane in intercept form is,

xa+yb+zc=1

The intercepts that the plane makes on the axis is 1a,1b,1c

Let C denotes the centroid, then,

C=1a+0+03,0+1b+03,0+0+1c3

Therefore, the coordinates of the centroid will be 13a,13b,13c

Hence, the correct option is (C) 13a,13b,13c.


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