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Question

If the centroid of the tetrahedron OABC, where A,B,C are given by (α,5,6),(1,β,4), (3,2,γ) respectively is (1,1,2), then value of α2+β2+γ2 equals

A
α2+β2
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B
γ2+β2
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C
α2+γ2
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D
α3+β3
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Solution

The correct option is B γ2+β2
The centroid of tetrahedron having vertices O(0,0,0),A(α,5,6),B(1,β,4) and D(3,2,γ) is
=(0+α+1+34,0+5+β+24,0+6+4+γ4)=(1,1,2) (given)
(α+44,β+74,γ+104)=(1,1,2)
Equating respective coordinate, we get α=0,β=11,γ=2
So clearly α2+β2+γ2=β2+γ2, since α=0.

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