Let L is a line of intersection of `x+2y+z=6` and `y+z=4`. If P`(alpha,beta,gamma)` is foot of perpendicular from (3,2,1) on L then Find `21(alpha+beta+gamma)`

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 .

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 = ______

If alpha, beta, gamma are the zeros of the polynomial x^(3)-6x^(2) -x+ 30 then (alpha beta+beta gamma + gamma alpha) = ?

If alpha,beta,gamma are the cube roots of p then for any x,y and z(x alpha+y beta+z gamma)/(x beta+y gamma+z alpha) is

If alpha,beta,gamma are the cube roots of p, then for any x,y,z(x alpha+y beta+z gamma)/(x beta+y gamma+z alpha)=