Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5, which is perpendicular to the plane x - y + z = 0.

Explanation

Given the equation of the plane through the intersection of the plane x+y+z=1 and 2x+3y+4z=5 is `(x+y+z−1)+λ(2x+3y+4z−5)=0`


=` (2λ+1)x+(3λ+1)y+(4λ+1)z−(5λ+1)=0.`.....(1)


The direction ratios a,b,c​ of this plane are `(2λ+1),(3λ+1) and (4λ+1)`


The plane in equation (1) is perpendicular to x−y+z=0

so,
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