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Question

# A plane meets the coordinate axes at points A, B, C and (α,β,γ) is the centroid of the triangle ABC. Then the equation of the plane is

A

xα+yβ+zγ=3

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B

xα+yβ+zγ=1

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C

3xα+3yβ+3zγ=1

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D

αx+βy+γz=1

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Solution

## The correct option is A xα+yβ+zγ=3 Let the co-ordinates of the points where the plane cuts the axes be (a,0,0), (0,b,0) and (0,0,c). Since the centroid is (α,β,γ), we have a= 3α,b= 3β,c= 3γ The equation of the plane will be xa+yb+zc=1⇒x3α+y3β+z3γ=1⇒xα+yβ+zγ=3

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