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

Options

A. `20x+23y+26z=0`
B. `20x+23y+26z+69=0`
C. `20x+23y+26z-69=0`
D. None of the above

Answer

C

Explanation

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