An equation of the plane passing through the line of intersection of the planes x+y+z=6and 2x+3y+4z+5=0 and passing through (1, 1, 1) is

Equation of any plane through the line of intersection of the given planes is 2x+3y+4z+5+λ(x+y+z−6)=0It passes through( 1, 1, 1)if (2+3+4+5)+λ(1+1+1−6)=0⇒λ=14/3 and the required equation is therefore,20x+23y+26z=69.