question_answer 29)

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. 

Answer:

Equation of plane passing through the intersection of x + y + z = 1 and 2x + 3y + 4z = 5 is       (x + y + z ? 1) +  (2x + 3y + 4z ? 5) = 0       x + (1 + ) y + (1 + ) z + (?1 ?5) = 0                                                             ..( 1)                       But it is perpendiular to plne x ? y + z = 0        (1 + 2) + (?1) (1 + 3) + 1 (1 + 4) = 0                     Put  in equation (1), we get                    x ? z + 2 = 0