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Find the equation of plane passing throu...

Find the equation of plane passing through the intersection of plane `2x + 3y + 4z - 5 = 0` and 3x + 4y - 7z + 8 =0 and also passing through (1, 2, 3).

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We know that equation of plane passing through intersection of `A_(1)x + B_(1)y+C_(1) z-d_(1)=0 and A_(2)x+B_(2)y+C_(2)z-d_(2)=0` is given by
`(A_(1)x + B_(1)y+C_(1) z-d_(1)) +lambda ( A_(2)x+B_(2)y+C_(2)z-d_(2))=0`
`(2x+3y+4z-5)+lambda (3x+4y - 7z +8)=0`
passes through (1, 2, 3) so
`(2 + 3 + 4 - 5) + lambda (3 + 4 - 7 + 8) = 0`
`4 + 8 lambda = 0`
`lambda = -1/2`
`(2x + 3y + 4z -5) - 1/2 (3x + 4y - 7z +8) =0`
`x + 2y + 15z-18 = 0`
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