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Question

If a plane meets the coordinate axes at A,B and C such that the centroid of the triangle is (1,2,4), then the equation of the plane is


A

x+2y+4z=12

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B

4x+2y+z=12

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C

x+2y+4z=3

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D

4x+2y+z=3

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Solution

The correct option is B

4x+2y+z=12


Explanation for the correct option:

Finding the equation of the plane:

Given,

Centroid of the triangle =1,2,4

Assume three points on the co-ordinate axes are A=a,0,0,B=0,b,0andC=0,0,c

Therefore, a3=1a=3

b3=2b=6

c3=4c=12

we know that, equation of the plane is

xa+yb+zc=1

x3+y6+z12=1

4x+2y+z=12

Hence, option "B" is correct.


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