Question

find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0

Answer 1

Plane passes through the intersection of tje two line
(x+y+z-1)+k(2x+3y+4z-5)=0........................1
Equ 1 perpendicular to the plane x-y+z=0
=> the normal of both the normal is also perpendicular to each other
aa'+bb'+cc'=0
1.(1+2k)-1.(1+3k)+1.(1+4k)=0
1+3k=0
K=-1/3
Put it back into the 1 u get the equation of the line passes to the intersection of the planr