The foot of perpendicular from `(1,2,6)` to line `(x-3)/2=(y+1)/2=(z-1)/(-1)` is the point `(alpha,beta,gamma)` then `(alpha+beta+gamma)=`

Let (alpha, beta, gamma) be the foot of perpendicular from the point (1, 2, 3,) on the line frac{x 3}{5} = frac{y - 1}{2} = frac{z 4}{3} then 19 (alpha beta gamma)

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

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 system of linear equations given by x+y+z=3 2x+y-z=3 x+y-z=1 is consistent and if (alpha ,beta,gamma) is a solution then 2alpha+2beta+gamma = ______

alpha,beta, gamma roots of 4x^(3)+8x^(2)-x-2=0 then value of (4(alpha+1)(beta+1)(gamma+1))/(alpha beta gamma)

The equations of the line through the point (alpha, beta, gamma) and equally inclined to the axes are (A) x-alpha=y-beta=z-gamma (B) (x-1)/alpha=(y-1)/beta=(z-1)/gamma (C) x/alpha=y/beta=z/gamma (D) none of these

Let L be a line obtained from the intersection of two planes x+2y+z = 6 and y+2z=4 . If point P(alpha,beta,gamma) is the foot of perpendicular from (3,2,1) on L then the value of 21(alpha+beta+gamma) equals .

alpha,beta,gamma roots of 4x^(3)+8x^(2)-x-2=0 ,then value of (4(alpha+1)(beta+1)(gamma+1))/(alpha beta gamma) is

If cos ^(-1) alpha+cos ^(-1) beta+cos ^(-1) gamma=3 pi then alpha(beta+gamma)+beta(gamma+alpha)+gamma(alpha+beta)=

The equations of the line through the point (alph, beta, gamma) and equally inclined to the axes are (A) x-alphay-beta=z-gamma (B) (x-1)/alpha=(y-1)/beta=(z-1)/gamma (C) x/alpha=y/beta=z/gamma (D) none of these