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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

`20x+23y+26z-69=0`

B

`20x+26y+23z-69=0`

C

`x+y+z-3=0`

D

`2x+3y+4z-9=0`

Text Solution

Verified by Experts

The equation of the plane through the line of intersection of the given planes is
`(x+y+z-6)+lamda(2x+3y+4z+5)=0` ………..i
If it pases through (1,1,1) we have
`-3+14lamda=0implieslamda=3//14`
Putting `lamda=3//14` in i we obtain the equation of the required plane as `20x+23y+26z-69=0`
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