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

Question

If the centroid of the tetrahedron OABC, where A, B, C are given by (α, 5, 6), (1, β, 4), (3, 2, &gamma;) respectively be (1, -1 ,2), then value of α2+β2+&gamma;2 equals (A) α2+β2 (B) &gamma;2+β2 (C) α2+&gamma;2 (D) 0

Tardigrade Admin · Accepted Answer

Centroid of tetrahedron, x = (x1+x2+x3+x4/4) or 1 × 4 =α+1+3+0 or α=0 ∴ α2+β2+&gamma;2 = β2+&gamma;2 (as α=0)

Q. If the centroid of the tetrahedron $O A BC$ , where $A, B, C$ are given by $(α, 5, 6), (1, β, 4), (3, 2, γ)$ respectively be $(1, - 1, 2)$ , then value of $α^{2} + β^{2} + γ^{2}$ equals

$α^{2} + β^{2}$

$γ^{2} + β^{2}$

$α^{2} + γ^{2}$

$0$

Centroid of tetrahedron, $x = \frac{x _{1} + x _{2} + x _{3} + x _{4}}{4}$
or $1 \times 4 = α + 1 + 3 + 0$
or $α = 0$
$∴ α^{2} + β^{2} + γ^{2} = β^{2} + γ^{2}$ (as $α = 0)$

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

α2+β2

γ2+β2

α2+γ2

0

Centroid of tetrahedron, x=4x1​+x2​+x3​+x4​​ or 1×4=α+1+3+0 or α=0 ∴α2+β2+γ2=β2+γ2 (as α=0)

Q. If the centroid of the tetrahedron $O A BC$ , where $A, B, C$ are given by $(α, 5, 6), (1, β, 4), (3, 2, γ)$ respectively be $(1, - 1, 2)$ , then value of $α^{2} + β^{2} + γ^{2}$ equals

$α^{2} + β^{2}$

$γ^{2} + β^{2}$

$α^{2} + γ^{2}$

$0$

Centroid of tetrahedron, $x = \frac{x _{1} + x _{2} + x _{3} + x _{4}}{4}$
or $1 \times 4 = α + 1 + 3 + 0$
or $α = 0$
$∴ α^{2} + β^{2} + γ^{2} = β^{2} + γ^{2}$ (as $α = 0)$