Equation of any plane passing through (1,2,1) is ‌A(x−1)+B(y−2)+C(z−1)=0 ⇒Ax+By+Cz=A+2B+C ⇒(‌
A
A+2B+C
)x+(‌
B
A+2B+C
)y ‌+(‌
C
A+2B+C
)z=1 According to the question, ‌‌2A+3B+C=0 . . . (ii) −A+2B−3C=0 . . . (iii) From Eqs. (ii) and (iii), A=−11,B=5,C=7 ∴A+2B+C=−11+10+7=6 From Eq. (i), −‌
11
6
x+‌
5
6
y+‌
7
6
z=1 . . . (iv) On comparing Eq. (iv) with ax+by+cz=1, we get a=−‌