Let the mirror image of the point (a, b, c) with respect to the plane 3x – 4y + 12z + 19 = 0 be `(a-6, beta, gamma)`. If a + b + c = 5, then `7beta -9gamma` is equal to _______

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

If the image of the point ( 1,-2,3) in the plane 2x + 3y -z =7 is the point ( alpha, beta , gamma ), then the value of alpha + beta + gamma is equal to

Let a, b in R . If the mirror image of the point P(a, 6, 9) with respect to the line (x-3)/(7)=(y-2)/(5)=(z-1)/(-9) is (20, b, -a -9), then |a + b| is equal to :

Let the equation of the plane, that passes through the point (1, 4, - 3) and contains the line of intersection of the planes 3x - 2y + 4z -7 = 0 and x + 5y - 2z + 9 = 0, be alphax + betay + gammaz+3=0 , then alpha + beta + gamma is equal to :

Let alpha , beta , gamma , delta be real numbers such that alpha^(2) +beta^(2) +gamma^(2) != 0 and alpha +gamma = 1 . Supose the point (3,2,-1) is the mirror image of the point (1,0,-1) with respect to the planet alphax + beta y + gammaz = delta . Then which of the following statements is/are TRUE ?

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

If the mirror image of the point P(3, 4, 9) in the line (x-1)/3=(y+1)/2=(z-2)/1 is (alpha, beta) then the value of 14(alpha+beta+gamma) is.

Mirror image of point (1,3,5) w.r.t plane 4x-5y+2z=8 is (alpha,beta,gamma) then 5(alpha+beta+gamma)

Let alpha,beta,gamma be the complex roots of x^(3)-1=0 then,alpha+beta+gamma is equal to

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