If the mirror image of the point `(1,3,5)` with respect to the plane `4x-5y+2z=8` is `(alpha. beta,gamma),` then `5(alpha+beta+gamma)` equals:

Find the the image of the point (alpha, beta, gamma) with respect to the plane 2x+y+z=6 .

A variable plane is at constant distance 3 from origin and meets the axis in X,Y,Z planes through X,Y,Z parallel to coordinate planes are made. If P be the point of intersection of above made planes, given P(alpha, beta, gamma) then (alpha beta gamma)/(sqrt(alpha^(2)beta^(2)+beta^(2)gamma^(2)+gamma^(2)alpha^(2)))=?

If the point (2 , alpha , beta) lies on the plane which passes through the points (3,4,2) and (7,0,6) and is perpendicular to the plane 2x-5y=15, then 2 alpha - 3 beta is equal to:

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 …..........

The equation of plane parallel to the plane x+y+z=0 and passing through (alpha, beta, gamma0 is (A) x+y+z=alpha+beta+gamma (B) x+y+z=alphabeta+betagamma+gammaalpha (C) x+y+z+alpha+beta+gamma=0 (D) none of these

If alpha, beta ,gamma are the roots of the equation x ^(3) + 2x ^(2) - x+1 =0, then vlaue of ((2- alpha )(2-beta) (2-gamma))/((2+ alpha ) (2+ beta ) (2 + gamma)) is :

If the direction angles of a line are alpha, beta and gamma respectively, then cos 2 alpha + cos 2 beta + cos 2gamma is equal to

If alpha, beta and gamma are the roots of the equation x^(3)+x+2=0 , then the equation whose roots are (alpha- beta)(alpha-gamma), (beta-gamma)(beta-gamma) and (gamma-alpha)(gamma-alpha) is

If alpha, beta, gamma and delta are the roots of the equation x ^(4) -bx -3 =0, then an equation whose roots are (alpha +beta+gamma)/(delta^(2)), (alpha +beta+delta)/(gamma^(2)), (alpha +delta+gamma)/(beta^(2)), and (delta +beta+gamma)/(alpha^(2)), is:

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