Plane ax+by+cz+1=0 passes through (1,−2,1) ∴a−2b+c+1=0.....(1) Plane ax+by+cz+1=0 is perpendicular to 2x−2y+z=0 ⇒2a−2b+c=0.......(ii) Also, perpendicular to x−y+2z=4 ⇒a−b+2c=0.....(iii) From Eqs. (ii) and (iii),
−c
2
+2c=0 ⇒c=0 From Eq. (i), a−2b=−1 From Eq. (ii), a−b=0 or a=b ∴b−2b=−1 Or −b=−1⇒b=1 a=1 Now, a+b−c=1+1−0=2