`(-4,9,6),(-1,6,6),(0,7,10)` are vertices of a triangle whose angles are `alpha,beta,gamma` and `alpha,beta,gammagt 0,` then a possible value of `alpha+beta-gamma` is

If cos(alpha+beta)sin(gamma+delta)=cos(alpha-beta)sin(gamma-delta) then the value of cot alpha cot beta cot gamma, is

If [(0,2beta,gamma),(alpha,beta,-gamma),(alpha,-beta,gamma)] is orthogonal, then find the value of 2alpha^(2)+6beta^(2)+3gamma^(2).

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

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 …..........

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 zeros of the polynomial x^(3)-6x^(2)-x+30 then the value of (alpha beta+beta gamma+gamma alpha) is

P(cos alpha,sin alpha),Q(cos beta,sin beta),R(cos gamma,sin gamma) are vertices of triangle whose orthocenter is (0,0) then the value of cos(alpha-beta)+cos(beta-gamma)+cos(gamma-alpha) is

If alpha+beta+gamma=6,alpha^(2)+beta^(2)+gamma^(2)=14 and alpha^(3)+beta^(3)+gamma^(3)=36, then alpha^(4)+beta^(4)+gamma^(4)=

If alpha, beta, gamma are the cube roots of 8 , then |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|=

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