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)` .

Explanation

Here, The equation of the plane through the line of intersection of the given planes is `(x+y+z-6)+lambda(2 x+3 y+4 z+5)=0 ldots ldots ldots . .1`

If it pases through (1,1,1) ,

we get,


`-3+14 lambda=0 Rightarrow lambda=3 / 14`


Putting `lambda=3 / 14` in i we obtain the equation of the required plane as


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