question_answer 27)

Find the equation of the plane through the intersection of the planes 3x –y + 2z – 4 = 0 and x + y + z – 2 = 0 is and the point (2,2,1). 

Answer:

Let the required equation of the plane through the intersection  of planes 3x - y + 2z - 4 = 0 and x + y + z ? 2 =0 is  (3x ? y + 2z ? 4) + K (x + y + z ? 2) = 0       (K + 3) x  (K ? 1) y + (K + 2) z ? 2K ? 4 = 0   .. (1)       Since it passed through point (2, 2, 1)        (K + 3) (2) + (K ? 1) (2) + (K + 2) (1) ? 2K ? 4 = 0                   Put  in (1), we get       = 0