The origin is the centroid of `/_\ABC` with the vertices `A(alpha, 1, 3),B(-2, beta, -5) and C(4,7,gamma)` find the values of `alpha, beta, gamma`.

If origin is the centroid of /_\ABC with the vertices A(alpha, 1,3),B(-2,beta, -5) and C(4,7,gamma) find the value of alpha, beta,gamma

If the centroid of a triangle with vertices (alpha, 1, 3), (-2, beta, -5) and (4, 7, gamma) is the origin then alpha beta gamma is equal to …..........

If the centroid of triangles formed by the vertices (1, 2, 3), (2, 1, 0) and (3, 1, 4) is (alpha, beta, gamma) then the value of [alpha]+[beta]+[gamma], where [ ] represents the greatest integer function, is _______.

If the centroid of the tetrahedron O-ABC, where A-=(alpha,5,6), B-=(1,beta,4) and C-=(3,2,gamma) is G(1,-1,2) , then: alpha^(2) + beta^(2) + gamma^(2)=

If origin is the orthocentre of the triangle with vertices A(cos alpha,sin alpha),B(cos beta,sin beta),C(cos gamma,sin gamma) then cos(2 alpha-beta-gamma)+cos(2 beta-gamma-alpha)+cos(2 gamma-alpha-beta)=

alpha , beta , gamma are the roots of the equation x^(3)-3x^(2)+6x+1=0 . Then the centroid of the triangle whose vertices are (alpha beta,1/(alpha beta)) , (beta gamma, 1/(beta gamma)) , (gamma alpha,1/(gamma alpha)) is

If alpha,beta,gamma are the real roots of the equation x^(3)-3ax^(2)+3bx-1=0 then the centroid of the triangle with vertices (alpha,(1)/(alpha))(beta,(1)/(beta)) and (gamma,1/ gamma) is at the point

If the roots of 4-3x+5x^2+x^3=0 are alpha,beta,gamma then the value of 1/alpha+1/beta+1/gamma= ________ .

Let cos(alpha-beta) + cos(beta - gamma) + cos(gamma - alpha)= -3/2 , then the value of cos alpha + cos beta + cos gamma is

Delta ABC has vertices A(a cos alpha,a sin alpha),B(a cos beta,a sin beta) and C(a cos gamma,a sin gamma) then its orthocentre is