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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)` .

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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`
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