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

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

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.

Let (alpha,beta,gamma) be the mirror image of the point (2,3,5) in the line (x-1)/(2)=(y-2)/(3)=(z-3)/(4) .Then, 2 alpha+3 beta+4 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 ?

The variance of alpha,beta and gamma is 9, then variance of 5 alpha, 5 beta, 5 gamma is

Suppose (alpha,beta,gamma) lie on the plane 2x+y+z=1 and [alpha,beta,gamma][(1,9,1),(7,2,1),(8,3,1)]=[0,0,0] then alpha +beta^(2)+gamma^(2) = _____

If reflection of A(1, -10, 1) about the line frac{x-1}{2} = frac{y-1}{3}=frac{z-2}{5} is (alpha, beta, gamma) then the |2 alpha 3 beta 5 gamma| is

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= ________ .

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