A plane meets the coordinate axes #A, B, C# such that the centroid of the triangle #ABC# is the point #(a, b, c)#, show that the equation of the plane is #x/a+y/b+z/c=3#?

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Answer 1 · 2017-07-07T09:24:20

See the proof below

The equation of the plane is

#x/A+y/B+z/C=1#

By the definition of the centroid

#(A/3,B/3,C/3)=(a,b,c)#

Therefore,

#A=3a#

#B=3b#

#C=3c#

The equation of the plane becomes

#x/(3a)+y/(3b)+z/(3c)=1#

#1/3(x/a+y/b+z/c)=1#

So,

#x/a+y/b+z/c=3#