[" If for some "alpha" and "beta" in "R" ,the "],[" intersection of the following three planes "],[x+4y-2z=1,x+7y-5z=beta],[x+5y+alpha z=5" is a line in "R^(3)," then "alpha+beta" is "],[" equal to "]

If plane x + 4y - 2z = 1, x + 7y – 5z = beta, x + 5y + alphaz = 5 intersects in a line (R xx R xx R) then alpha + beta is equal to

If plane x + 4y - 2z = 1, x + 7y – 5z = beta, x + 5y + alphaz = 5 intersects in a line (R xx R xx R) then alpha + beta is equal to

For real numbers alpha and beta , consider the following system of linear equations: x+y-z=2, x+2y+alpha z=1, 2x- y+z= beta . If the system has infinite solutions, then alpha+beta 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 :

If the line (x-2)/(3)=(y-1)/(-5)=(z+2)/(2)" lies in the plane "x+3y-az+beta=0" then "(alpha,beta) is

If x = sin alpha, y = sin beta, z = sin (alpha + beta) then cos (alpha + beta) =

If the line (x-2)/3 =(y-1)/-5 =(z+2)/2 lies in the plane x+3y - alphaz + beta=0 , then: (alpha, beta)-=

For real numbers alpha and beta ne 0 , if the point of intersection of the straight lines ( x - alpha)/( 1) = ( y - 1)/( 2) = ( z -1)/( 3) and ( x - 4) / ( beta) = ( y - 6)/( 3) = ( z - 7)/(3) , lies on the plane x + 2y - z = 8 then alpha - beta is equal to