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 _______.

The circumcentre of a triangle having vertices A(a,atan alpha),B(b,btan beta),C(c,ctan gamma) is at origin, where alpha+beta+gamma =pi . Then the orthocentre lies on

If alpha , beta, gamma are the roots of x^3+x^2-5x-1=0 then alpha+beta+gamma is equal to

Find the area of the triangle whose vertices are : (a cos alpha, b sin alpha), (a cos beta, b sin beta), (a cos gamma, b sin gamma)

If tan alpha, tan beta, tan gamma are the roots of equation x^3 - 3ax^2 + 3bx - 1 =0 , find the centroid of the triangle whose vertices are (tan alpha, cot alpha), (tan beta, cot beta) and (tan gamma, cot gamma) .

cos alpha sin (beta-gamma) + cos beta sin (gamma-alpha) + cos gamma sin (alpha-beta)=

If alpha, beta gamma are the real roots of the equation x^(3)-3px^(2)+3qx-1=0 , then find the centroid of the triangle whose vertices are (alpha, (1)/(alpha)), (beta, (1)/(beta)) and (gamma, (1)/(gamma)) .

Determine the values of alpha ,beta , gamma when [{:( 0, 2beta, gamma),( alpha ,beta, -gamma),( alpha ,-beta, gamma):}] is orthogonal.

If 2 sin alphacos beta sin gamma=sinbeta sin(alpha+gamma),then tan alpha,tan beta and gamma are in

If alpha + beta + gamma = π/2 and cot alpha, cot beta, cot gamma are in Ap. Then cot alpha. Cot gamma