Find the equation of the plane containing the line of intersection of the planes x + y + z - 6 = 0 and 2x + 3y + 4z + 5 = 0 and passing through the point `(1,1,1)`

Explanation

The equation of a plane passing through the line of intersection of the given planes is
`" "(x+y+z-6)+lamda(2x+3y+4z+5)=0" "`(i)
If it is passes through (1, 1, 1), (1+1+1-6) +`lamda`(2+3+4+5)=0, then
`" "lamda=(3)/(14)`
Putting `lamda=3//14` in (i) , we get
`" "(x+y+z-6)+(3)/(14)(2x+3y+4z+5)=0`
`" "20x+23y+26z-69=0`