TS EAMCET 4-Aug-2021 Shift 2 Question Paper

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