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Find the equation of a plane containing ...

Find the equation of a plane containing the line of intersection of the planes `x+y+z-6=0a n d2x+3y+4z+5=0` passing through `(1,1,1)` .

A

`x+y+z=3`

B

`x+2y++3z=6`

C

`2x+3y+4z=9`

D

`3x+4y+5z=18`

Text Solution

Verified by Experts

The correct Answer is:
B
Equation of plane containing the line of intersection of planes is
`(x+y+z-6)+lamda(2x+3y+4z-12)=0`
Since, it passes through the point (1,1,1).
`:." "(1+1+1-6)+lamda(2+3+4-12)=0`
`rArr" "-3+lamda(-3)=0`
`rArr" "lamda=-1`
Hence, required equation of plane is
`(x+y+z-6)-(2x+3y+4z-12)=0`
i.e. `x+2y+3z=6`
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